dimensional travel power

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Dimensional Travel

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The power to travel between different dimensions . Combination of Dimensional Manipulation and Teleportation .

• 1 Also Called
• 2 Capabilities
• 3 Applications
• 4 Variations
• 5 Associations
• 6 Limitations
• 7.1 Anime/Manga/Manhwa
• 7.2 Cartoons
• 7.5 Literature
• 7.6 Live Television
• 7.9 Video Games
• 7.10 Web Comics/Original/Series
• 8.1 Anime/Manga/Manhwa
• 8.2 Cartoons/Comics
• 8.3 Live Television/Movies
• 8.4 Literature
• 8.5 Video Games
• 8.6 Web Animation/Comic/Original/Series
• 9.1 Anime/Manga/Manhwa
• 9.2 Cartoons/Comics
• 9.3 Live Television/Movies
• 9.5 Video Games
• 9.6 Web Comics

Also Called [ ]

• Cross-Time Jump/Jumping/Teleportation/Transportation/Travel/Traveling
• Dimension/Realm Hopping/Jumping/Travel/Traveling
• Dimensional/Universal Jump/Jumping/Teleportation/Transportation/Travel/Traveling
• Interdimensional/Inter-Reality Jump/Jumping/Teleportation/Transportation/Travel/Traveling
• Parallel World/Universe/Reality Jump/Jumping/Teleportation/Transportation/Travel/Traveling

Capabilities [ ]

The user can travel between different dimensions and universes, and cross over different planes of existence or travel across various forms of reality.

The user can travel to alternate universe/other earths and/or even (pocket) dimensions.

Applications [ ]

• 4th Wall Breaching
• Afterlife Traveling
• Alternate Reality Traveling
• Alternate Timeline Traveling
• Beforelife Traveling
• Book Jumping
• Chronoskimming
• Dimensioskimming
• Dimensional Transformation
• Fantasy Travelling
• Fiction Travel
• Instant Transmission
• Multiversal Travel
• Reality Crossroads
• Reality Shifting
• Realm Connection
• Spatial Travel
• Time Travel
• Time-Window Alteration
• Black Hole / White Hole Creation
• Fissure Creation
• Dimensional Storage
• Portal Attacks
• Absolute Attack
• Mass Teleportation
• Partial Teleportation
• Tactile Teleportation
• Warping Teleportation

Variations [ ]

• Planeswalking ; Mystical version

Associations [ ]

• Powerful Objects
• Alien Physiology
• Dimensional Manipulation
• Dimension Shifting
• Distance Manipulation
• Planes Dreaming
• Speedster Physiology
• Teleportation
• Unbound Soul

Limitations [ ]

• May not have control over when they travel between worlds.
• Initiating the transportation may take time or have other specific recommendations.
• May only be able to travel to a specific dimension.
• Can still be affected by Warp Travel Unravel and Warp Travel Interaction .
• Can be unable to enter worlds that are restricted from access.

Known Users [ ]

See Also: Dimensional Traveler

Anime/Manga/Manhwa [ ]

• Drago ( Bakugan: Battle Brawlers )
• Wavern ( Bakugan: Battle Brawlers )
• Mechtogans ( Bakugan: Battle Brawlers )
• Skull Knight ( Berserk )
• Griffith/Femto ( Berserk )
• Conrad Leto ( Black Clover )
• Shinigami ( Bleach ); via "Senkaimon"
• Hollows & Arrancar ( Bleach ); via "Garganta"
• Quincy ( Bleach ); via "Shadow"
• Shinobu Negero ( Buso Renkin )
• Road Kamelot ( D.Gray-man )
• All Spirits ( Date A Live )
• Mastemon ( Digimon )
• Quantumon ( Digimon )
• Sorcerers ( Dorohedoro )
• Supreme Kais
• Touka ( Fairy Tail: 100 Years Quest)
• Faris ( Fairy Tail: 100 Years Quest)
• Selene ( Fairy Tail: 100 Years Quest)
• Misaki ( Fairy Tail: 100 Years Quest)
• Road Dopant ( Futo Detective ) via using high-temperature heat and high speed
• Gods ( In Another World with my Smartphone )
• Endymion ( In Another World with my Smartphone )
• Velgrynd ( That Time I Got Reincarnated as a Slime )
• King Ghidorah ( Godzilla: The Planet Eater )
• Guido-Hyun ( The Haunted House/Shinbi Apartment )
• Kibi ( The Haunted House/Shinbi Apartment )
• Funny Valentine ( JoJo's Bizarre Adventure Part VII: Steel Ball Run ); via Dirty Deeds Done Dirt Cheap/D4C
• Vanilla Ice ( JoJo's Bizarre Adventure Part III: Stardust Crusaders ); via Cream
• Dimension ÄRM users ( Marchen Awakens Romance )
• IV (Vier) ( Marchen Awakens Romance )
• Pandora ( Monster Strike )
• Users of Kamui ( Naruto )
• Users of Yomotsu Hirasaka ( Naruto )
• Sasuke Uchiha ( Naruto )
• Kinshiki Ōtsutsuki ( Naruto )
• Nue ( Boruto: Naruto Next Generations )
• Users of Kama Rift ( Boruto: Naruto Next Generations )
• Users of Claw Mark ( Boruto: Naruto Next Generations )
• Blueno ( One Piece ); via Doa Doa no Mi
• Blast ( One-Punch Man )
• Gemini Saga ( Saint Seiya )
• Sideways ( Transformers Unicron Trilogy )
• Galvatron ( Transformers Unicron Trilogy )
• Soundwave ( Transformers Unicron Trilogy )
• Vector Prime ( Transformers Unicron Trilogy )
• 'Emperor' Starscream ( Transformers Unicron Trilogy )
• Anyone with the Omega Lock. ( Transformers Unicron Trilogy )
• Mokona ( Tsubasa Reservoir Chronicle )
• Itsuki ( Yu Yu Hakusho )
• Kazuma Kuwabara ( Yu Yu Hakusho )
• Users of Interdimensional Travel Technology ( Yu-Gi-Oh ARC-V )
• Yubel ( Yu-Gi-Oh GX )
• Gorm ( Zatch Bell! )
• Mirage ( Aladdin: The Animated Series )
• Gwen Tennyson
• Verdona Tennyson
• Maltruant ( Ben 10: Omniverse )
• Diagon ( Ben 10: Ultimate Alien )
• Eon ( Ben 10 Series )
• Flame Keepers' Circle Soldiers ( Ben 10: Ultimate Alien )
• Professor Paradox ( Ben 10 Series )
• Vilgax ( Ben 10: Ultimate Alien ); temporally???
• Sam Wilson/Falcon ( Marvel's Avengers Assemble ) briefly via Runestone
• Alya Césaire/Ubiquity ( Miraculous World: Paris )
• Monrach/Gabriel Agreste
• Marinette dupain-Chang/Ladybug/Ladybiquity ( Miraculous ladybug )
• Brutaka ( Bionicle ); via Kanohi Olmak
• Vezon ( Bionicle ); via Kanohi Olmak
• Catbug ( Bravest Warriors )
• Dr. Dimensionpants ( Dr. Dimensionpants )
• Four-dimensional space whales ( Futurama )
• Breach ( Generator Rex )
• Bill Cipher ( Gravity Falls ); only through people’s imagination/mind
• Fiddleford Hadron McGucket ( Gravity Falls )
• Grim ( The Grim Adventures of Billy and Mandy )
• Invisible Dragon ( Invisible Dragon )
• Te Xuan Ze ( The Life & Times of Juniper Lee )
• Doomagedoon ( League of Super Evil )
• Mot ( Mot )
• Rick Sanchez ( Rick and Morty ); via portal gun
• Star Butterfly ( Star vs. the Forces of Evil ); in butterfly form
• Hekapoo ( Star vs. the Forces of Evil )
• Cyborg ( Teen Titans Go! )
• Primus ( Transformers )
• Unicron ( Transformers )
• Skywarp ( G1 Transformers )
• The Sorcerer
• The Sorceress
• Uncle Grandpa ( Uncle Grandpa )
• Black Hat ( Villainous )
• Eliotropes ( Wakfu )
• Sirenix Fairies ( Winx Club ); to Infinite Ocean
• Mythix Fairies ( Winx Club ); to Legendarium World
• Tynix Fairies ( Winx Club ); to MiniWorlds
• Onyrix Fairies ( World of Winx ); to World of Dreams
• Blunk ( W.I.T.C.H ); via Tooth of the Tonga
• Elyon Brown ( W.I.T.C.H. )
• The Mage ( W.I.T.C.H ); via her Ring
• Nerissa ( W.I.T.C.H )
• Will Vandom ( W.I.T.C.H )
• Cosmic Owl ( Adventure Time )
• Cosmo and Wanda ( Fairly Odd Parents )
• Fat Chance ( The Venture Bros )
• Master of Games ( Teen Titans )
• Ixis Naugus ( Archie's Sonic the Hedgehog )
• Zone Cops ( Archie's Sonic the Hedgehog )
• Users of the Speed Force ( DC Comics )
• Kryptonians ( DC Comics ); via yellow sun radiation
• The Herald ( DC Comics ); via Gabriel's Horn
• Monarch ( DC Comics )
• Raven ( DC Comics )
• Grail ( DC Comics )
• New Gods ( DC Comics ); via Mother Box that can generate Boom Tubes
• Sideways ( DC Comics )
• Supernova ( DC Comics )
• Vibe ( DC Comics )
• Breacher ( DC Comics )
• The Anti-Monitor ( DC Comics )
• The Batman Who Laughs ( DC Comics )
• The Phantom Stranger ( DC Comics )
• Superboy-Prime ( DC Comics )
• Alexander Luther Jr ( DC Comics )
• Metron ( DC Comics )
• Mr Mxlylplx
• Zauriel ( DC Comics ); via Michael's Sword
• Folding Man ( DC Comics )
• The Endless ( DC/Vertigo Comics )
• Starbreaker ( DC Comics )
• The Carrier ( Wildstorm/DC Comics )
• Spawn ( Image Comics )
• Angstrom Levy ( Image Comics )
• Beyonders ( Marvel Comics )
• Captain Britain Corps ( Marvel Comics )
• The Exiles ( Marvel Comics )
• Loki Laufeyson ( Marvel Comics )
• Thor Odinson ( Marvel Comics ); via Mjolnir
• Doctor Stephen Strange ( Marvel Comics )
• Ancient One ( Marvel Comics )
• Doctor Victor Von Doom ( Marvel Comics )
• Magik ( Marvel Comics )
• Lockjaw ( Marvel Comics )
• Great Weaver ( Marvel Comics )
• Inheritors ( Marvel Comics )
• Onslaught ( Marvel Comics )
• Pathway ( Marvel Comics )
• Quasar ( Marvel Comics )
• Mojo ( Marvel Comics )
• Spiral ( Marvel Comics )
• Shatterstar ( Marvel Comics )
• Rachel Summers ( Marvel Comics )
• Nate Grey/X-Man ( Marvel Comics )
• Wiccan ( Marvel Comics )
• America Chavez ( Marvel Comics )
• The Impossible Man ( Marvel Comics )
• Combo Man ( Marvel Comics )
• Mother ( Marvel Comics )
• Access ( Marvel/DC/Amalgam Comics )
• Omni-Viewer ( Sonic the Comic )
• Voyd ( The Incredibles 2 )
• Jack Jack Parr ( The Incredibles )
• Malevolent Mame ( The Chase 3: Great Minds Think Alike )
• John Constantine ( Constantine )
• Joe Talbot ( Crossworlds )
• Stygian demons ( Dogma )
• The Tall Man ( Phantasm )
• Spot ( Spider-Man: Across the Spider-Verse )
• Demogorgons ( Stranger Things )
• Fallen/Megatronus Prime ( Transformers Revenge Of The Fallen )
• Jetfire ( Transformers: Revenge of the Fallen )
• Sentinel Prime ( Transformers: Dark of the Moon ); via Space Bridge technology
• Ancient Primes ( Transformers: Revenge of the Fallen )
• Ransack ( Transformers: Revenge of the Fallen )
• Seekers ( Transformers: Revenge of the Fallen )
• Fortress ( Transformers: Revenge of the Fallen )
• Initiates of the Pattern, the Logrus, and of Broken Patterns; some demons ( The Chronicles of Amber )
• Hoid ( Cosmere )
• Nac Mac Feegle ( Discworld series )
• Ragnor Fell ( The Mortal Instruments )
• Jonathan Christopher Morgenstern ( The Mortal Instruments )
• Oswald Bastable, Una Persson ( A Nomad of the Time Streams )
• Travelers ( Pendragon )
• Red & Randy Dorakeen ( Roadmarks )
• Ciri ( The Witcher )
• Cthulhu ( Cthulhu Mythos )
• Mr. Munshun/Lord Malshun ( Black House )

Live Television [ ]

• Tobias Ford ( Agents of SHIELD )
• The Beast ( Angel )
• Illyria ( Angel )
• Mistress Meerna ( Angel )
• Willow Rosenberg ( Buffy the Vampire Slayer )
• D'Hoffryn ( Buffy the Vampire Slayer )
• Mok'tagar Demon ( Buffy the Vampire Slayer )
• Elders ( Charmed )
• Tyler Michaels ( Charmed )
• The Source of All Evil ( Charmed )
• Whitelighters ( Charmed )
• Omega ( Doctor Who )
• Anala ( The Elephant Princess )
• Louie Preston ( The Haunted Hathaways ); via to Portal Creation / Door Projection
• Olivia Dunham ( Fringe )
• Kelli Wheaton ( Heroes )
• Jefferson ( Once Upon a Time )
• Chunky Chicken ( Mighty Morphin Power Rangers )
• Octomus the Master ( Power Rangers Mystic Force )
• Nighlok ( Power Rangers Samurai )
• Goldwinger ( Power Rangers Ninja Storm )
• Danny ( Tripped )
• Quinn Mallory ( Sliders ); via Timer
• Wade Welles ( Sliders ); via Timer
• Rembrandt Brown ( Sliders ); via Timer
• Maximillian Arturo ( Sliders ); via Timer
• Maggie Beckett ( Sliders ); via Timer
• Angus Rickman ( Sliders ); via Timer
• Colin Mallory ( Sliders ); via Timer
• Quinn "Mallory" Mallory ( Sliders ); via Timer
• Diana Davis ( Sliders ); via Timer
• Kromaggs ( Sliders )
• Demogorgon ( Stranger Things )
• Alex Russo ( Wizards of Waverly Place )
• Choju ( Ultraman series )
• Galactron ( Ultraman series )
• Ultraman Zero ( Ultraman series )
• Barry Allen/The Flash
• Eobard Thawne/The Reverse Flash
• Hunter Zolomon/Zoom
• Cisco Ramon/Vibe
• Mar Novu/The Monitor ( Arrowverse )
• The Music Meister ( Arrowverse )
• Plastoid ( Arrowverse )
• Edwin Gauss/Folded Man ( Arrowverse )
• Clifford DeVoe/The Thinker ( Arrowverse/The Flash 2014 )
• Tsukasa Kadoya ( Kamen Rider Decade/Zi-O )
• Daiki Kaito ( Kamen Rider Decade/Zi-O )
• Narutaki ( Kamen Rider Decade )
• DJ Sagara ( Kamen Rider Gaim )
• Ra’jah O’Hara ( Rupaul’s Drag Race ); as I'Siya Queen through dancing.
• Witches ( The Vampire Diaries/The Originals/Legacies ) via spells
• Ziltoid the Omniscient ( Devin Townsend Project )
• Choerry/Choi Yerim ( LOOΠΔ Kpop Girl Group)
• The Planeswalkers ( Magic the Gathering )
• Neo the Magic Swordsman ( Yu-Gi-Oh! )

Video Games [ ]

• Player ( Pixel Worlds )
• Shadow Man ( Call of Duty )
• The Baker ( Cookie Clicker )
• Morrigan Aensland ( Darkstalkers )
• Dante ( Devil May Cry/DmC )
• Arkham ( Devil May Cry )
• Mundus ( Devil May Cry )
• Vergil ( Devil May Cry )
• Azimuth ( Legacy of Kain )
• Kain as Scion of Balance ( Legacy of Kain )
• Raziel ( Legacy of Kain )
• Divayth Fyr ( The Elder Scrolls III: Morrowind )
• Gilgamesh ( Final Fantasy V )
• The Gods ( Genshin Impact )
• Celestial Twins ( Genshin Impact )
• Riku/Riku-Ansem ( Kingdom Hearts ); via darkness
• Elfilin (Kirby and the Forgotten Land)
• Kassadin ( League of Legends )
• Croire ( Hyperdimension Neptunia )
• Ganondorf ( The Legend of Zelda )
• Midna ( The Legend of Zelda: Twilight Princess )
• Yabusame Houlen ( Len'en Project )
• Major Sybil Tan/Kestrel ( Marvel Strike Force )
• IDPD - the Interdimensional Police Department ( Nuclear Throne )
• Palkia ( Pokémon )
• Giratina ( Pokémon )
• Time Eater ( Sonic Generations )
• Mephiles the Dark ( Sonic the Hedgehog )
• Shadow the Hedgehog ( Sonic the Hedgehog )
• Sonic the Hedgehog ( Sonic the Hedgehog )
• Erwin Reanna Schrodinger ( Honkai Impact 3rd )
• Lord Vortech ( LEGO Dimensions )
• All Playable Characters ( LEGO Dimensions )
• Anne von Blyssen ( Starshine Legacy )
• Culex ( Super Mario RPG: Legend of the Seven Stars )
• Count Bleck ( Super Paper Mario )
• Dimentio ( Super Paper Mario )
• Turok ( Turok: Dinosaur Hunter )
• Kishua Zelretch Schweinorg ( TYPE-MOON )
• Dream Phantom ( Valkyrie Crusade )
• Dimension Hacker ( Valkyrie Crusade )
• Various Magic Users ( Warcraft series )
• Elizabeth Comstock ( Bioshock Infinite )
• Boys of silence ( Bioshock infinite )
• Add ( Elsword )
• Aisha ( Elsword )
• Jesse Faden ( Control ); via Slide Projector
• Dylan Faden ( Control ); via Slide Projector
• Polaris ( Control ); via Slide Projector
• The Hiss ( Control ); via Slide Projector
• Robloxians ( ROBLOX )
• Herrscher Of The Void ( Honkai impact 3rd )
• Lucifer ( Helltaker )
• Boyfriend ( Friday Night Funkin )
• Girlfriend ( Friday Night Funkin )
• Steve/Alex/Player ( Minecraft ); via Nether Portal or End Portal
• The Ink Demon ( Bendy and the Ink Machine/Dark Revival )
• The Traveler ( Just Dance )
• Nessie ( Hungry Shark Evolution )
• Behellmouth ( Hungry Shark Evolution )

Web Comics/Original/Series [ ]

• Baron von Mouse ( Dog Cat Mouse )
• Everywhere ( Jenny Everywhere )
• Various Characters ( Order of the Stick )
• The Entity ( AT4W )
• Scion/Zion ( Worm )
• Eden (Worm)
• Mechakara ( AT4W )
• Lord Vyce ( AT4W )
• Dr. Linksano ( AT4W )
• Dr. Insano ( The Spoony Experiment )
• Nox Decious ( Stupid Mario Brothers )
• Mecha Sonic ( Super Mario Bros. Z )
• The G-Man ( Half-Life Series )
• Noclippers ( The Backrooms )
• Calvin Lucien/O5-1 ( SCP Foundation ); via Dr. Wondertainment’s Interdimensional Line and Lure
• The Fifth Overseer/O5-5 ( SCP Foundation )
• The Brothers Death ( SCP Foundation )
• SCP-001 - Tufto's Proposal - The Scarlet King ( SCP Foundation )
• SCP-507 - Reluctant Dimension Hopper ( SCP Foundation )
• SCP-993 - Bobble The Clown ( SCP Foundation )
• SCP-3022 - Hooked on a Feeling ( SCP Foundation )
• SCP-3167 - Character Assassin ( SCP Foundation )
• SCP-3319 - The Clusterfuckalypse ( SCP Foundation )
• SCP-3396 - The Empyrean Parasite ( SCP Foundation )
• Mortimer J. Denning Von Kronecker ( SCP Foundation )
• Cartoon Cat
• Yoru ( Valorant )
• Wraith ( Apex Legends )
• Error Sans ( Errortale )
• Salad Fingers ( Salad Fingers ); via Puddles

Known Objects [ ]

See Also: Interdimensional Travel Device

Anime/Manga/Manhwa

• Gatekeeper Pierrot ( Marchen Awakens Romance )
• Yamato ( Devil May Cry )
• Nebula Chain ( Saint Seiya )
• Mao's Magic Mirror ( Shining Tears x Wind )
• Dungeon Keys ( Solo Leveling )
• Road Memory ( Futo Detective )
• Portal to Sonic's world ( Sonic X ); only between Earth and Sonic's world
• Gogoukanda ( Twelve Kingdoms )

Cartoons/Comics

• Enchiridion ( Adventure Time )
• Prismo’s Remote ( Adventure Time )
• Portal Spell ( American Dragon: Jake Long )
• Calamity Box ( Amphibia )
• Null Void Projector ( Ben 10 )
• Gabriel's Horn ( DC Comics )
• Mother Box ( DC Comics )
• Mobius Chair ( DC Comics )
• Infi-Map ( Danny Phantom )
• Fenton Ghost Portal ( Danny Phantom )
• Zandora's Box ( Dungeons & Dragons: The Animation )
• The Super-Collider ( Into the Spider-Verse )
• Realm Crystal ( Lego Ninjago: Masters of Spinjitzu )
• Traveler's Tea ( Lego Ninjago: Masters of Spinjitzu )
• Dimensional Travel Watch ( Marvel Comics )
• Mjolnir ( Marvel Comics )
• Multisect ( Marvel Comics )
• Siege Perilous ( Marvel Comics )
• Space Gem ( Marvel Comics )
• Nexus of All Realities ( Marvel Comics )
• Runestones ( Marvel's Avengers Assemble )
• Crystal Mirror/Statue portal ( My Little Pony: Equestria Girls )
• Titan's Blood ( The Owl House )
• Portal Gun ( Rick and Morty )
• Heart of Etheria ( She-Ra and the Princesses of Power )
• Youtube Remote ( SMG4 )
• Dimensional Scissors ( Star vs. the Forces of Evil )
• Grim's Scythe ( The Grim Adventures of Billy and Mandy )
• Interdimensional Portal & Porta-Portal ( The Jimmy Timmy Power Hour III: The Jerkinators! )
• Recall Potion ( Wakfu )
• Magic Watches ( Winx Club )
• Heart of Kandrakar ( W.I.T.C.H )
• Parallel Universe Box ( Futurama )
• Yin Yang Yoyo ( Xiaolin Showdown )
• Stanford’s portal ( Gravity Falls )
• Interdimensional Rift ( Gravity Falls )
• Closet doors ( Monsters, Inc. ); only between the Monster World and Human World
• The Second Star to the Right ( Disney's Peter Pan ); only between Earth and Neverland
• Magical Box ( We Baby Bears )

Live Television/Movies

• Breaches ( Arrowverse )
• Pylean Book ( Angel )
• Sling Rings ( Marvel Cinematic Universe )
• Tesseract ( Marvel Cinematic Universe )
• The Tardis ( Doctor Who )
• The Thinker’s Hoverchair ( Arrowverse/The Flash )
• Timer ( Sliders )
• Wishing Well ( Enchanted )
• Rings ( Sonic the Hedgehog Movie )
• Crystal Elevator ( Thea Stilton )
• Wardrobe ( The Chronicles of Narnia )

Video Games

• Lor Starcutter ( Kirby )
• Phantom Ruby ( Sonic the Hedgehog )
• Mirror Of Twilight ( The Legend of Zelda: Twilight Princess )
• Nether Portal ( Minecraft )
• End Portal ( Minecraft )
• Slideshow Projector ( Control )
• Voyagers ( What Lies in the Multiverse )

Web Animation/Comic/Original/Series

• Dr. Wondertainment's Interdimensional Line and Lure ( SCP Foundation )
• Backroom Keys ( The Backrooms )

Gallery [ ]

Cartoons/Comics [ ]

Live Television/Movies [ ]

Web Comics [ ]

• 1 Superpowers
• 2 List of Kinetic Abilities
• 3 Darkness Manipulation

Deepwoken Wiki

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Dimensional Travel

• View history
• 1 Description
• 2 Appearance
• 3.1 Resonance Points
• 5 Tips/Trivia
• 6 Navigation

Description [ ]

Dimensional Travel , also referred to as Kamui , or Distortion Realm , is a Resonance or "bell" that players can obtain and is exceedingly rare to roll.

Appearance [ ]

On usage, the user will leave behind a vortex-esque portal and be transported into a realm called The Interstice , where surfaces are dark, the fog is heavy, and abandoned, destroyed buildings lay.

Pressing C will activate the Dimensional Travel Resonance.

When activated, the user is transported into an alternate dimension known as The Interstice , and will briefly leave a lingering portal to allow other players to enter. The resonance cannot be activated if the user is in combat, unless the Use in Combat Resonance stat is invested into. Each step taken inside The Interstice will translate to a varying amount of steps taken outside of The Interstice, depending on your resonance point allocation.

Dimensional Travel cannot be used in the Etris Palace , Voidheart , Duke Erisia's Manor , or instanced dungeons.

The function activating the Resonance has is dependent on what state of 'using the resonance' you're in:

• If any players inside The Interstice jump into the void through the cracks in the floor or get downed, they will be teleported to the equivalent overworld position.
• After ~10 seconds, the user's camera moves back to their character and ends the 'visual indicator' state automatically. This can be ended early by moving your character.
• If activated whilst the visual indicator is active, the user creates a portal in The Interstice leading to the location from the visual indicator, effectively completing the usage cycle.

Resonance Points [ ]

When obtained, Dimensional Travel will spend it's Resonance points on the following stats:

• Use in Combat: If this stat is invested into, the user can use the Resonance while in combat. Deducts a sizeable amount of Resonance points
• Capacity: The more points that are invested into this stat, the higher the amount of players that can enter the realm before the portal automatically closes.
• Whilst in The Interstice , you can view your current location in the overworld by opening your map, which will accurately show your equivalent overworld location.
• An explanation (and a way to find your distance multiplier) can be found in the Deepwoken Info Discord .
• Despite being obsolete with the introduction of the map mechanic, you can use this Google document to travel using coordinates. You can view your coordinates by pressing Shift + F3, then Shift + 1 four times.

If Dimensional Travel is Drowned, in addition to the extra Resonance points to spend, the Use in Combat stat is given by default.

Gallery [ ]

Tips/Trivia [ ]

• Like Portals , Dimensional Travel can be very useful in ambushing/ganking other players.
• Similar to Minecraft's Nether travel mechanics, both allowing extra distance to be covered in the overworld by traversing a distance in a separate dimension.
• Despite looking like a better than average area for combat, it is incredibly dangerous to fight in The Interstice while in the First Layer , as being forcefully teleported out of the realm by falling into an opening or being downed and being above the void can result in an instant wipe.
• When in the First Layer , if you leave the map and fall out of the world or get stuck inside of terrain, it will act as a reset and spawn you at one of the spawn locations.
• If used properly, timing a jump to change the angle of your momentum can allow you to gain great amounts of distance in a desirable direction over a short time.
• If you get teleported to the Voidheart due to a Voidwalker bounty expiring, you get teleported into the Voidsea (presumably the Voidheart's coordinates multiplied by your Dimensional Travel distance stat).
• Random Encounters from the Voidsea can briefly occur when arriving to or leaving The Interstice , due to your character being in the Voidsea for a short period.
• Gravity inside the Distortion Realm used to be reduced.
• There used to be a bug where buildings could be found in the Distortion Realm.
• Functions similar to Naruto character, Tobi/Obito's Mangekyou Sharingan Dōjutsu "Kamui" ability.
• You cannot climb the structures in The Interstice .

Navigation [ ]

• 2 Enchantments

Dimensional Travel

• View history

Klarion Bleak traveling from Earth to Limbo Town through a dimensional portal.

Sometimes confused with "teleportation" or "portals", Dimensional Travel is the ability to bodily pass from one reality into another through an act of will. Certain characters with this power are able to open portals or teleport with direct control of their destination and others may be limited to specific destinations.

Dimensional travel can be very dangerous:

• Traveling to the Antimatter Universe , for example, generates a chain reaction between matter and antimatter that creates a powerful explosion .
• A mere glimpse of the Hell dimension could drive someone insane.
• In Fairyland , science, even a simple chemical reaction such as an ordinary match-strike, can not work.
• Persons banished to the Phantom Zone will exist as disembodied ghosts.
• Teleportation
• Time Travel

All items (498)

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Dimensional Traveler

• View history

A Dimensional Traveler is any character who can (more or less) freely travel between various planes of existence, like parallel universes, etc. Their ability to travel is usually powered by some form magic, Applied Phlebotinum or Teleporters and Transporters (like a Portal Network ), but it can also happen that a character was inherently born with such power.

This is also a common explanation for Crossovers , as occasionally the characters will arrive in the universe of another hero.

Distinct from Time Travel because, although Time is considered the "fourth dimension", time travellers otherwise remain in the same plane while hopping between its different time periods.

See also Planar Champion .

• 1 Collectible Card Game
• 2 Fan Works
• 4 Literature
• 5 Live Action TV
• 6 Tabletop Games
• 7 Video Games
• 8 Western Animation

Collectible Card Game [ ]

• Magic: The Gathering . A mage is a planeswalker , able to travel to other planes of existence. The card battles between players represent encounters between planeswalker mages.
• In the Yu-Gi-Oh! card game, this is the premise of the D. D. (Different Dimension) cards. Also, while not part of the D. D. set, Neo the Magic Swordsman is described as a dimensional drifter on his card.

Fan Works [ ]

• It happens alot in Super Milestone Wars and it's sequel, Super Milestone Wars 2 .
• Also Wataru, Kuyou and a different, Evil Twin Kanae, who have been chasing her since long ago.
• The protagonist of Sleeping with the Girls , although he doesn't do it voluntarily. Every time he goes to sleep, he slips into another dimension ( and into the bed of another girl , usually with a Tsundere personality).
• Delilah from The Legend of Spyro a New Dawn is a Kitsune capable of traveling through dimensions. This apparently a species trait of her specific type of Kitsune, as it's the only way to leave the Spirit World. After 200 years of traveling the multiverse, she's a Genre Savvy Cloudcuckoolander whose Seen It All . She often drops Shout Outs to other series which she's visited, most commonly My Little Pony Friendship Is Magic because she really likes that universe and is best friends with Pinkie Pie. She also mentions the "Cupcakes Incident" frequently, which involved a nasty encounter with Cupcakes !Pinkie Pie and resulted in her being deathly afraid of cupcakes.
• In Indiana Jones and the Kingdom of the Crystal Skull , the Aliens were actually travellers between the worlds .
• The Phineas and Ferb made-for-TV film "Phineas and Ferb across the 2nd Dimension" is all about this.

Literature [ ]

• Also in another of his stories, The Number of the Beast . The protagonists use a dimension-hopping device to explore a series of very odd dimensions, including some based on Earth literature.
• Keith Laumer 's Lafayette O'Leary novels. The protagonist has the ability to travel to feudal/magical alternate Earths.
• In the Myth Adventures series, the term "Demon" is short for this.
• Philip Jose Farmer 's World of Tiers series. Paul Janus Finnegan (AKA Kikaha the Trickster) and Robert Wolff spend much of the novels traveling through artificially created universes.

Live Action TV [ ]

• Kamen Rider Decade has this as a major plot point. The previous seasons are revealed as parallel worlds that are merging into one, thus leading everyone of them to destruction, so it's up to the titular hero to journey to each one and destroy them . He even arrived in the World Of Shinkenger on one occasion. The reason being Decade normally travels to RIDER Worlds, and there aren't any Kamen Riders normally in that world until Diend went there, implying there's even more universes than just the Rider Worlds, but only the Rider Worlds are at risk.
• Sliders is a series based on this trope, although in the beginning the characters were travelling uncontrollably.
• Was quite common in The Flash before the Cosmic Retcon .

Tabletop Games [ ]

• The people that are seen on the Planescape setting. Many Planar characters use portals on a regular basis to travel between Sigil and the Outer Planes .
• Part and parcel of becoming a Planeswalker , before or after the Mending.

Video Games [ ]

• Tessa from Red Earth is a sorcerologist (one who employs magic in everyday studies to discern the properties of the universe; she's more or less a witch, though). Her knowledge on a wide variety of subject matter in both her home series and various crossovers imply that she frequently treks across the multiverse to broaden her horizons and learn as much as she possibly can.
• In Darkstalkers , the only thing linking the Human World and Makai ( the Demon World ) is a portal located roughly in the middle of Makai, known as The Gate. Morrigan is a special case, in that she can freely travel between the realms independently of this gateway. Being a fun - loving succubus , you should be able to understand why she enjoys this unique ability of hers.
• This is the reason why Gilgamesh in Final Fantasy is heavily implied to be the only recurring character in the series to be the same exact character in most, if not all appearances. After being thrown into the Interdimensional Rift by his boss Exdeath for his repeated losses against the party and sacrificing himself to defeat Necrophobe , Gilgamesh simply walks the multiverse via the Void and the worlds connected to it. This is even how he stumbles into the conflict of the gods in Dissidia 012: Final Fantasy ; when defeated, a portal leading to the Rift/Void engulfs him, as Gilgamesh, while subject to the war's rules, has no original world to return to .
• The Elder Scrolls III: Morrowind - Divayth Fyr is said to be one. According to the in game book The Doors of Oblivion , Fyr is one of the few "mortals" who can freely travel between the realms of the Daedra .
• Axl Low from Guilty Gear . And I-No.

Western Animation [ ]

• The Road to the Multiverse Episode of Family Guy has Brian and Stewie fulfilling this role.
• The third season of Transformers: Cyberverse introduces the Quintessons who travel the Multiverse with ease. Megatron steals one of their ships and somehow gains unusual powers while travelling eternity. The finale features an alternate version of Megatron who defeated the Quintessons and stole their technology, using it to cross over to the main timeline.
• Rick and Morty in Rick and Morty . In the third season finale, Rick outright says that he, and his infinite counterparts, scuttle across the multiverse like hermit crabs.
• 1 Low Tide in Twilight/Characters
• 2 Kuroinu Kedakaki Seijo wa Hakudaku ni Somaru/Characters
• 3 Metamorphosis (manga)

Dimensional Travel

Concept » Dimensional Travel appears in 1372 issues .

Whether by magic or by science, this is the ability to move from one dimension into another.

Summary short summary describing this concept..

Angstrom Levy

Angstrom Levy was a man with the ability to travel to alternate realities who had a horrific accident with the technology that allowed him to do so. He blames Invincible for this and has since become a very serious recurring threat to him.

The once-mysterious Cable (a.k.a. Nathan Summers) is Cyclops' time-traveling son who was infected with the deadly techno-organic virus during his infancy, which he keeps at bay using his advanced psionic powers. At one time a founding member and leader of the militant team called X-Force, previously known as the New Mutants, Cable takes the aimless youths under his wing and whips them into fighting shape in order to prepare them for future threats.

Dabbling in forbiden sorcery destroyed Tuoni's body, leaving only the vengeance-seeking phantasm known as Dominus.

She is an immortal god in the DC universe. She guided the Man of Steel in his path of righteousness. She has had limited appearances since then.

The younger sister of Colossus. Illyana Rasputin is a mutant teleporter, a sorceress, and the ruler of Limbo, who is currently a member of Storm's team of mutants residing in the "Jean Grey Institute for Higher Learning".

Man-Thing is a powerful swamp creature and guardian of the Nexus of all Realities. He was once human and turned himself into a monster as a last act of defense and a way too avoid his serum falling in the wrong hands.

Mr. Fantastic

Reed Richards, also known as Mr. Fantastic, is the leader of the Fantastic Four. He can stretch his body to great distances due to his exposure to cosmic rays while in space. He is also considered to be one of the smartest men alive, using his brain to explore alternate dimensions and save the world alongside his family from science-based threats.

Gambit from an alternate reality in which he attained his power's full potential.

Nightcrawler

Kurt Wagner is a prominent member of the X-Men and former member and leader of Excalibur. He possessed the Neyaphemian ability of teleportation, as well as incredible agility, wall scaling and a prehensile tail. Nightcrawler is a devout Catholic, contrasting his demonic appearance. He is a highly skilled swordsmen and former circus acrobat.

Director of A.R.M.O.R., Charles Little Sky is a mutant with the power to create portals to other dimensions.

The insane son of Moira MacTaggert, Proteus is a mutant with the power to warp the fabric of reality itself. He must constantly hop from body to body, as the energies he controls burn out living flesh rapidly.

Member of the very powerful race known as the Q continuum, Q has been a thorn in the side of various Starfleet Captains, including Picard, Sisko, and Janeway.

The Tall Man

The Tall Man is the antagonist of the Phantasm film and comic book series.

Trevor Fitzroy

Fitzroy is a mutant from Earth-1191 with the ability to absorb a person's life force and create a space or time portals.

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http://tvtropes.org/pmwiki/pmwiki.php/Main/InterdimensionalTravelDevice

Interdimensional Travel Device

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A device that allows travel between dimensions/alternate universes/planes of existence/etc . This device could be anything, from a machine in science fiction to a magical item or spell in fantasy, as long as it allows travel between these dimensions or realities. It could even be a human (or, at the very least, a sentient being), if they have the power to go to these other "places".

There may be lots of Fridge Logic involved, depending on the nature of the device in question. For example, in the version shown in the image, where you open up a portal that doesn't need to be attached to the surface of a flat object, how do you ensure that the other end is always exactly at the surface of the desired planet (as opposed to high in the air or deep underground), and perpendicular to the ground? And if you decide to go exploring universes you've never been to prior (and thus have no data on what things are in it and where), how do you avoid, say, destroying your home planet by accidentally opening the other end in the interior of a sun? And even if you decide to be cautious about it, how do you gather data on said universe without actually opening a portal and sending a drone or probe in first?

Compare Time Machine and Inn Between the Worlds . If the device is bladed, it's a Dimensional Cutter .

See also Dimensional Traveler for someone who tends to use these.

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• Bleach : There are three methods to travel between worlds. Shinigami use Senkaimon, a highly regulated gate which provides direct travel between the Human World and Soul Society. To use it, one must follow a special butterfly called Jigokucho, or else they will be thrown to Dangai, the Void Between the Worlds . Traveling through Dangai can eventually lead someone into either world, but they have to be extremely careful not to stick themselves to a current is inescapable or face a being that is unbeatable. The third method is to use Garganta, which cracks open the dimensional fabric and is associated with Hollows. Garganta is the only way to access Hueco Mundo.
• This is one of the Jewel Pod's (from the Jewelpet franchise) many functions.
• The Lyrical Nanoha franchise has Casual Inter-Dimensional Travel , with various Magitek starships allowing those who can't perform sufficient magic to go travel to different dimensions. Supplementary material set after Magical Girl Lyrical Nanoha A's Portable : The Gears of Destiny also had the Eltria group discovering a piece of Lost Technology that allowed them to move people from one Alternate Multiverse to another, a function they learned after some irresponsible handling of the newly discovered artifact caused it to pull in The Movie continuity version of Nanoha and Fate.
• Negima! Magister Negi Magi 's Chao Lingshen eventually will has developed one of these, allowing characters to hop from one time-travel-created timeline to the next.
• Phantasy Star Online 2 has the titular Phantasy Star Online 2 , which serves as a link between Earth and the dimension that the video game that the anime is based off of takes place in. It's also a Stealth Prequel .
• Red Ash: Gearworld has the parallel machine, which is a huge device propped up on three legs that fires a beam sending hunters to parallel worlds. Said hunters must be under the machine when it fires, since it fires downward.
• In Yugioh Arc V having as a main plot an interdimensional war has several of them are around, from the duel disks of the Fusion and Xyz dimensions inhabitants, and after Reiji got ahold of Yuto's duel disk he was able to implement the same feature on the Lancers (Standard) disks using cards to set up coordinates also during the first season it was already known that Yuzu's bracelet note  It's unknown if the other bracelets have a similar feature could warp people away, but during the Battle Royale it warped her and Yugo to the Synchro Dimension and in the same vein the Yugo's Clear Wing Synchro Dragon has been doing that to him for a while now, its implied that the four Dimensional Dragons have the same power as well, because they are drawn to each other .
• Naruto : This is Obito Uchiha's main Mangekyo Sharingan ability, Kamui. Both of his eyes can send something to a Pocket Dimension . His right eye is a defense mechanism, being used so Obito can travel to the dimension at will. He can even send parts of his body when in danger so he could dodge at the last second, giving the illusion that he is an Intangible Man . His left eye, which was given to Kakashi Hatake, is the offensive version of the same ability. Namely, it can teleport someone or something to the pocket dimension.
• SD Gundam Force has the Zakurello Gate, which is primarily used by the Dark Axis to invade Neotopia's dimension. The SDG spends most of the series trying to build their own device, but ultimately just use the Zakurello Gate after the main invasion.
• Magic 's original villains, the Phyrexians, had devices called Ambulators which created portals to any plane.
• The Talon Gates were created in the aftermath of the first Planeswalker Duel on Dominaria, from the loser's corpse. It allowed planar travel to some extent, but there aren't many details on exactly how it functioned. It's beleived to at least have allowed consistent travel between Dominaria and Kamigawa .
• After the Mending, all previous Planeshifting devices stopped working. The only new device developed since the Mending was Rashmi's Planar Bridge, and that can't transport living matter unless it's a planeswalker anyway. As it turns out, Nicol Bolas only needed it to transport an army of the dead from Amonkhet to Ravnica . After the War of the Spark ended, it currently remains in the hands of Tezzeret.
• RASL : Dr. Robert Joseph Johnson jumps between parallel worlds using an immersion suit, a device that looks like 4 airplane turbines strapped to his shoulders and legs with an African mask covering his face.
• Atari Force : The ship Scanner One is equipped with a Multiverse warp drive that allows its passengers to travel through both normal space and multiple alternate dimensions.
• The Dark Judges possess orbs that allow travel between dimensions, which they stole from a group of aliens who made the mistake of visiting their world. Justice Department later reverse engineers the technology to create their own dimensional teleporters. In the "Helter Skelter" story they're forced to destroy their own D-jump technology after a nearly successful invasion by Dredd's enemies from other dimensions.
• Even earlier the Sov Mega-Cities developed Apocalypse Warp technology, which during the early stages of the Apocalypse War enabled them to redirect Mega-City One's nuclear counter-attack to another dimension, which was promptly destroyed . However, unlike the orbs brought over by the Dark Judges, it seems that the Apocalypse Warp could not be focused and only worked at random.
• Marvel Comics ' features plenty of casual multiversal travel - such technology is common in a technologically advanced universes, and from there it gets spread throughout the rest. Entire series such as Exiles and Web Warriors are built on the use of this trope, as are many other storylines such as The Avengers (Jonathan Hickman) , Spider-Verse and Contest of Champions (2015) .
• The Flash has the Cosmic Treadmill, which was first constructed when Barry Allen was trapped in the "real world" analogue called Earth-Prime and needed to return to Earth-1. It also appeared in Crisis on Infinite Earths a few times when the superheroes needed to bridge dimensional barriers between worlds.
• Monica's Gang : Marina's pencil allows her to travel to other worlds. Other characters stealing the pencil for themselves is what insigates various crossovers, a prominent example being Glu accidentally drawing a portal to Garfield 's universe in Turma da Mônica e Garfield: O Lápis Mágico .
• In the Thor / Being Human crossover series, Housemates , Dr. Strange devises one for Coulson's and Mitchell's universe hopping in the form of a smart phone app .
• In the Empath: The Luckiest Smurf story "Smurfed Behind: The Other Side Of The Mirror", a Magic Mirror known as the Janus Mirror transports Empath and his friend Polaris Psyche into a Mirror Universe version of their world, where they find an identical mirror which requires a magic spell to open so they could return to their own world.
• Metal Gear: Green : The HPSC gives Night Owl the green light for interdimensional exploration as they see it as a massive profit binge. Nine years later, and the only reason it isn't discontinued isn't because Night Owl's interdimensional explorations did bear some fruit ( he did teleport the MSF into the MHA world ), but because if it came out that they had Izuku as a battery, the HPSC would not only be dissolved on the spot, but most of the top brass would be executed as well.
• The Mountain and the Wolf : The Seafang (the Wolf's longship) is able to sail the Warp by opening a hole into it, going from universe to universe (or different areas of the same universe) with relative ease (relative applying to its crew, who are only protected from the daemons of the Warp by the efforts of the warriors fending them off) and can even tow ships behind it. It can also fly, negating the need to land in water. All in all, it behaves more like a Warhammer 40,000 starship than the original version , which was only implied to fly rather than shown and spews fog until it's surrounded by mists and daemons, then the fog (eventually) lifts and finds itself back in the real world.
• PMD: Another Perspective : Team Rocket has invented a machine that creates a portal to a world where only Pokemon exist. They plan on using it to abduct rare Pokemon from the other world and sell them for profit.
• In Phineas and Ferb The Movie: Across the 2nd Dimension the Other Dimension-inator is used by Heinz Doofenshmirtz to go to the second dimension, as the title suggests.
• Spider-Man: Across the Spider-Verse has the Dimensional Travel Watch, which were invented by Miguel O'Hara and are used by countless Spider-Mans to travel to different dimensions. It also prevents them from glitching while they’re visiting a dimension that they’re not from. Miles spends the first half of the movie trying to get one for himself, but Miguel refuses to give him one since Miles himself is a dimensional anomaly. The spider that he was bitten by was accidentally leaked into his dimension, thus Miles was never supposed to become a Spider-Man.
• The One has a quantum tunneling device which allows the interdimensional police to track criminals and, obviously, allows them to travel to different universes.
• Crossworlds has a staff which can get the main characters from the odd world from which the staff comes and back to what appears to be our Earth.
• Parallels has an entire derelict building that shunts people about randomly through the Multiverse . Best guess so far is that it was built by some sort of awesomely advanced version of humanity that's either forgotten about it or doesn't much care about the havoc it's wreaking across hundreds of alternate Earths.
• In the movie Cool World , the Spike of Power created by Dr. Vincent Whiskers. It can breach the boundary between the real world and the cartoon Cool World. It is, however, a potential Artifact of Doom in that it can actually tear down the walls between worlds completely, leading to the Roger Rabbit Effect on a massive scale — and not in a fun way.
• In the Paratime series by H. Beam Piper , the means of traveling through timelines is a conveyor using the Ghaldron-Hesthor field-generator. Conveyors are fixed in place, which means that as they travel through timelines, they may end up inside nuclear reactors or other hazards or be caught in warfare (a common activity on at least one timeline in nearly every trip, Paratimers note). Weakening of the transposition field is a concern of Paratimers.
• In The Number of the Beast , Professor Jacob Burroughs creates a device that allows travel between dimensions. It's installed in a vehicle and allows the protagonists to go on a series of adventures.
• The Dark Tower series has doors that allow the characters to travel between different timelines and alternate universes, including one in which they meet the author, Stephen King .
• The Lion, the Witch, and the Wardrobe : has a wardrobe that allows travel between Earth and Narnia — sometimes.
• Susan's horn has the power to summon help to the user, which includes help that just happens to be in another dimension, as shown in Prince Caspian .
• The Magician's Nephew has the green and yellow rings, which allow one to enter the Wood between the Worlds and leave there for any number of worlds. The rings are mentioned again in The Last Battle.
• The Transition Of Titus Crow has a clock that allows Titus Crow to travel to different dimensions.
• His Dark Materials has items that allow for interdimensional travel.
• The Kadingir series has the titular Kadingir technology, which opens portals to connect Earth with a parallel dimension. Ishtar activates one such devices by accident, thinking it was a Game Boy, and gets lost in planet Ki as a result.
• Myth Adventures has the D-Hopper which is used throughout the series to get to different universes.
• The Incomplete Enchanter by L. Sprague de Camp and Fletcher Pratt introduced the Syllogismobile which attuned the practitioners' minds to a selected alternate universe strongly enough to shift them into it.
• In Parallax Hominids by Robert J. Sawyer, decoherence created by a quantum computer sends the neanderthal Ponter to a universe very similar to our own.
• The Aleph from Spectral Stalkers , which can send the user from one random dimension to another. It's the only way to escape from the dreaded Spectral Stalkers, after all.
• In Philip José Farmer 's World of Tiers novels, people can travel between the artificial universes of the setting by using gates. Gates can be activated by various means, including tokens and playing music on a special horn.
• The Wheel of Time has Portal Stones which, among other things, will let people travel between parallel realities.
• The Long Earth by Terry Pratchett and Stephen Baxter. Interdimensional travel is performed by the use of a Stepper, the designs for which appeared online one day. Its components are common enough to be bought from the local shops, and it's apparently powered by a potato-battery. Also unique is the fact that, unlike most other examples where parallel universes may diverge in recent history but are still recognisably similar to our own Earth, the parallel universes of the Long Earth are wildernesses devoid of human life (although not necessarily of intelligent life). Only our own Earth evolved humans.
• The titular carnelian cube in The Carnelian Cube sends one into a parallel world based on their desires at the time one sleeps with it beneath their pillow. In order to leave to another world one must find its counterpart in that particular world.
• In Down The Bright Way by Robert Reed , Pre Cursors left behind The Bright, a one-dimensional path of travel between different planes of reality. The Wanderers use it to travel to different Earths, which diverged millenia prior; exploring, teaching, stabilizing, or mourning the dead worlds . The Bright's travel mechanisms are powered by a planet that has been converted into a massive fusion reactor , and the Wanderers state that the Bright is so energy expensive to operate that comparatively, colonizing the Milky Way in any one plane would be a much easier task despite the lack of Faster-Than-Light Travel .
• The Lord of the Rings : The One Ring can actually be reckoned as one. Gandalf states as much when he says the Ring (making the bearer invisible) serves as this, because the bearer then is carried into the realm of the unseen, although without taking the bearer anywhere physically. The "unseen" realm is juxtaposed right on top of the regular world. Frodo, while wounded by the Morgul knife, is able to see both worlds.
• Borgel : Borgel's car can travel though time-space-and-the-other, and they use it to travel through dimensions. An essential device for any time tourist.
• Isaac Asimov 's " Living Space ": This Earth developed dimensional travel technology instead of Casual Interstellar Travel , because the technology was too difficult. Homes are built on alternate Earths that never developed life as we know it . Devices are keyed to work with the front door and what is effectively the garage. A unique 'probability pattern' is used to describe each Earth.
• Johannes Cabal and the Fear Institute : The Silver Key from the Cthulhu Mythos creates a gateway for physical travel to the Dreamlands . However, it requires the mind of someone who has seen Things Man Was Not Meant To Know , transforming them bodily into the Gate and hopefully killing them in the process.
• Alice mainly uses Power Tattoos to travel between dimensions, but Naga also gives her some beads that do the same thing without some of the unpleasant side-effects.
• Johrlac Hive Minds use cosmic equations to open holes in reality, though this usually destroys the world they're leaving.
• In Craig Shaw Gardner's Cineverse Cycle, you can get to and travel between the worlds of the Cineverse by turning the dial of a Captain Crusader Decoder Ring and saying "See you in the funny papers!".
• The Frugal Wizard's Handbook for Surviving Medieval England : The whole premise of the setting is that there are infinite alternative dimensions that can be reached through portals.
• In The Starlore Legacy , the Malakians translate themselves from the Ruah to the physical realm and back using little phase-shifter devices on their belts.
• A number of metahumans are capable of opening breaches between parallel worlds. These include people with "vibe" powers (Cisco, his Earth-2 double, Gypsy) and speedsters. Eventually, Cisco manages to create a small device that can open a breach between Earth-38 and Earth-1, just in case Kara wants to visit Barry . In a crossover episode, Music Meister uses the device to get to Barry, although it's implied he doesn't actually need it and merely wants Mon-El to follow him there.
• In the Crisis Crossover event Crisis on Earth-X , the resistance on Earth-X creates a portal machine which will enable them to recruit help from other realities to overthrow the Nazi regime. Unfortunately, the Nazis discover the project and seize control of it, planning on using it to conquer other Earths as they did their own.
• Thirdspace introduced an ancient Vorlon artifact that turned out to be a jumpgate to yet another dimension unimaginatively described as "Thirdspace." It turns out this is not a good place to open doors to and they destroy the artifact in order to close the door again.
• Buffy the Vampire Slayer and Angel had at least one of these, Angel used it to travel to Jasmine's old home. And another was used to travel to Skip's holding dimension where Billy was being kept. The 'verse's portal books probably count as well.
• The Time Lords did this on a regular basis before the Time War.
• In "Inferno" , the TARDIS console transports the Doctor to a parallel universe where Britain is governed by Fascists.
• In the same episode, the Dalek-built Void Ship (that created the tear between realities) was designed to traverse the void, or the extradimensional space between universes. When it was in void transit mode, it was visible, but otherwise didn't exist (scans reported it as having no mass or dimension), and was described as creepy to look at. When the void transit functionality was switched off (just prior to the Daleks emerging), it "became" a normal vehicle with normal mass/etc.
• There are several "techniques" of universe-crossing in Fringe : Walter's portal, which causes both universes to begin collapsing; William Bell's technique by which he pulled Olivia into the AU (usually only works on hybrid Super Soldiers who are designed to survive the crossing; it worked on Olivia because of her Cortexiphan-enhanced physiology); and the natural way, which is achieved by groups of Cortexiphan Kids being guided by Walter (and of the three, is clearly the least dangerous, to dimensions and dimension-crossers, but not without its kinks). Besides crossing, Peter is able to use the device created to only work with his genetics to bridge the to universes creating an Inn Between the Worlds . This unlike the other devices such as Walter's portal device has no know negative side effects. Another less used method is the harmonic rods which create an equilateral triangle enveloping the subject on both sides, and have the rods vibrate at the same frequency, and two objects of approximately equal mass will exchange places in space-time. There are many ways to mess this up though, such as only placing the rods in one universe.
• The Man in the High Castle : Throughout the series, various characters are able to visit parallel universe through some form of meditation, causing the film reels showing these worlds to spread. In season 3, the Nazis build an interdimensional travel device through technological means in an abandoned mine, the Nebenwelt project, in order to conquer other worlds.
• In The Monkees 1997 ABC special, Hey, Hey, It's the Monkees , we learn that Mike had turned the Monkeemobile into a dimension machine (AND lowrider, of all things). It's even capable of transporting them back to The '60s .
• The Cyber Museum from MythQuest lets Alex and Cleo select a historical artifact and enter a myth associated with the culture it came from.
• Jefferson's hat in Once Upon a Time can be used to travel between the different worlds.
• Come Power Rangers Ninja Steel and the series' 25th Anniversary episode, it seems other Rangers have been developing a dimension-hopper of their own, called a Transportal Device, capable of traversing between variant timelines. Such a device, as pointed out in History of Power Rangers , makes future team-ups all the more simple from a meta-perspective, since the writers won't have any reason not to have the Rangers use it.
• "Parallel Universe" had the Holly Hop Drive bring them there after a calculation error.
• "Backwards" had a time hole bring them to a universe where time runs backwards.
• "Dimension Jump" introduced Ace Rimmer and his ship that could travel through dimensions.
• "Only The Good..." had a prisim laser that lead to a mirror universe.
• "Back To Earth" had a dimension cutter that employed the use of the ink from a dimension traveling monster that lead to a Real-World Episode . Only not, as much of the three-parter was an illusion and they never left the ship .
• "Skipper" had Kryten invent the Quantum Skipper, a dimension travel device based on information salvaged from a science lab they previously visited, which Rimmer then uses to find a universe where he thinks he'll be happier.
• There's the "Timer", several of which were actually used by the main characters (the original until about the midpoint of the series, the one from Egyptian World that they'd use until the end, and Colonel Rickman's Timer, important for season three's endgame). The Timer's job was to open wormholes between universes, and also to malfunction or get stolen , providing half the series' plots .
• The Kromaggs have a more advanced version, which they use to conquer human worlds. In their first episode, they use a device taken by one of the Sliders to track them down on another world. However, it turns out that they didn't invent sliding technology. It was given to them by Quinn's double (the one from the pilot) to escape from their Earth, where they were fighting with humans. Later on, they try to use human brains to build instantaneous portals that work on a different principle than sliding tech in order to bypass the Slidecage.
• The sequel series to Spellbinder has the Trans-Dimensional Bamboo Boat, made from some kind of woody material. It looks like a boat, and travels across dimensions.
• There's the "quantum mirror", which makes a few appearances in early episodes before being destroyed offscreen, on O'Neill's orders. In one episode, Daniel accidentally uses it to travel to another universe; in a later episode, alternate-universe versions of Carter and Kowalski come back through it, looking for refuge from the Go'a'uld invasion fleet that just arrived on Earth in their universe.
• A later episode has a strange phenomenon that causes hundreds of SG-1 teams from alternate realities to start popping up in the "main" SGC. It turns out that the phenomenon was caused by the first alternate SG-1 team to arrive, who wanted to steal the "main" reality's ZPM .
• An alternate McKay builds an "alternate reality drive" which has this function. The only problem is, it doesn't have an off switch or any way to control which reality it jumps into. This leads to one universe's worth of main characters being stranded in the wrong reality and another universe's worth dying of starvation before they can figure it out, before the actual main characters bootstrap on their research and discover a way to make it backtrack through the realities it came from (so they can at least get home, if not actually exploit the drive).
• Another episode has McKay try to use a device to generate unlimited energy by getting it from an alternate reality. Unfortunately, this ends up nearly destroying an inhabited universe, so the alternate McKay uses the "bridge" to cross over into the "main" reality. At the end of the episode, they send him back.
• In Star Trek , transporters under the right circumstances can be used to travel between dimensions. One way is to add a device to the transporter that reconfigures it for this use.
• Some theories suggest black holes, or rather wormholes within them, could act as this sending whatever fell into them often to another Universe. These ideas, however, have been put into doubt by later ones that state that either said wormhole would be unstable and close inmediately, so no interdimensional travel of any kind, or that said behavior is just a failure of our current understanding.
• The Amulet of the Planes is a powerful Magical Accessory that lets the wearer transport themself and others to any other Plane of existence. There's no limit on its use, but it requires an Intelligence test each time to target the correct destination.
• The Cubic Gate is a rare magic item that is keyed to six Planes of existence and can manifest a portal to any one of them at a time.
• Various editions have no shortage of Portal Doors and like devices, such as disguised Magic Mirrors , that transport their users across Planes. Some are "always on" while others onlly activate when a certain combination of objects (a "portal key") are presented to them.
• Module Q1 Queen of the Demonweb Pits . A temple in a Drow city has a mural of a starry sky. If the PCs pass through an image of Lolth and touch it, they will be transferred to the level of the Abyss where Lolth's Demonweb exists. Once there they can find doorways to alternate Prime Material Planes as well as the Abyssal level where Lolth's spider ship awaits them.
• Module X2 Castle Amber . The Gate of the Silver Keys takes the PCs from Glantri in the Known World to the dimension where the country of Averoigne exists.
• Pathfinder has magic items called planar keystones that allow the user to plane shift to a specific location on another plane. The book on planar adventures also outlines the material components of the plane shift spell as planar tuning forks and has alternative rules for them if the DM wishes to restrict travel between dimensions, or at least make it more difficult for the players..
• Paranoia had the Transdimensional Collapsatron, which allowed travel between dimensions in several adventures.
• One of the campaign settings for GURPS has the PCs as interdimensional travelers, using a variety of devices ranging from handhelds to gates to vehicles.
• Champions adventure The Great Supervillain Contest . The Crimson Claw's base had the power of interdimensional teleportation. It was originally a dimensional exploration ship: when it entered his home dimension, the Claw drained the Life Energy of the crew and stole it.
• One plot hook in Rocket Age involves a man going missing from his private room, with the only object of interest being a large wardrobe . His name? C. S. Lewis !
• The "chronoscooters" in Timemaster were time machines that could also move between different time lines.
• In BIONICLE , the Olmak can do this.
• In Chrono Cross , Serge uses Kid's astral amulet to travel between his world and the other world which was created 10 years ago due to a universal split where Serge is alive in one universe and dead in the other. See Schrödinger's Cat
• In Crash Twinsanity , the psychetron created by Dr. Neo Cortex can travel between Crash's world and the 10th dimension and most of the game is based around gathering the power crystals needed to power the device so Crash Bandicoot can get to the 10th dimension to save his world.
• The "ancient ruins" that are the goal of Touhou Yumejikuu ~ Phantasmagoria of Dim. Dream turn out to be a Hyperprobability Space Vessel used by Yumemi and Chiyuri to travel from their own world to Gensokyo in search of the secrets of magic.
• While not a device, there are two main methods shown in The Longest Journey and Dreamfall that allow travel between the various worlds. Shifters are people who physically travel via portal they themselves open. Normally they can only travel between Stark (the world of technology) and Arcadia (the world of magic). April actually had to fly into space in Stark in order to get to the Guardian's Realm via a wormhole of some sort. The sequel also introduces Dreamers, people who fall asleep in one world and project a physical double into another one. The reason both types of people are able to cross between worlds is because all these worlds used to be one until they were split up by powerful wizards and scientists with the help from some space dragons in order to keep the world from the being destroyed.
• In Total Distortion , alien teleporters randomly show up on Earth, which turn out to allow travel between millions of different dimensional planes, many of them based on Earth pop culture. Unusually, the people of Earth first use these machines to teleport freight around the world , since teleporting a human puts them in a 6-week coma, along with the fact that larger objects cost more energy to be transmitted.
• The Yamato Perpetual Reactor in Shin Megami Tensei IV . With just the correct push, it can also serve as a handy multiverse-crushing black hole-creating machine.
• In Ratchet & Clank . The Dimensionator. Created by the Lombaxes to end the Great War against the Cragmites, they allow its user to open portals to any dimension merely by telling the device what to find.
• In Phantasy Star Online 2 , Phantasy Star Online 2 serves as this, linking the dimension that hosts Oracle and ARKS to that of Earth.
• The titular book of Rakenzarn Tales , which can transport whoever reads the appropriate incantation contained within between their home world and the world of Rakenzarn.
• Legendary Pokémon of Pokémon Sun and Moon , Solgaleo and Lunala can open up a wormhole inbetween an unknown amount of dimensions. The first stage evolution, Cosmog, can also do this.
• The Realmwalkers of Rakenzarn Frontier Story possess a teleporter system in the record hall of their HQ which can send people to any world, provided they have the book that documents that world's history and can set the proper coordinates. Later, Makoto gains an app for his phone that allows him to teleport directly to the Chamber of Rakenzarn at any time.
• Kingdom Hearts features various means to travel between worlds, some riskier than others. The safest option is to use a Gummi Ship, although this becomes harder after the Gummi blocks that constitute the walls protecting all worlds are restored after the first game, as people now have to rely on Keyblade wielders to open hidden pathways called Gates. Another safe option is to cross special pathways called Lanes Between, but this is exclusive to Keyblade wielders. A less cumbersome but more riskier option is to use the Corridors of Darkness. While only people with control of darkness can conjure them, anyone can use them after that. However, exposing oneself to darkness without wearing a black cloak will lead to unfortunate side effects.
• Parodied in the Henry Stickmin Series game "Infiltrating the Airship". One of the options available in the game is the Transdimensionalizer. When Henry flips the switch, it transports him to the 1st Dimension (aka a single straight horizontal line in mathematics). And he can't return either since the switch flips up and down.
• Chapter 2, Season 5 of Fortnite : Battle Royale sees Agent Jones use a portal device to recruit hunters from different realities onto the Island, in order to prevent any of the locals from breaking out of the "Groundhog Day" Loop that they're trapped on.
• In Dragon Ball Multiverse , some guys called the Vargas have one; it drives the plot, as they're able to cross between universes (timelines). They come from a different universe than the one the protagonists live in, and they offer them a chance to participate in a tournament among fighters from different universes. One of them is hijacked by King Vegeta and the Saiyans of Universe 10 in a coup d'état. But this part of the plot is in a galaxy far, far away... and only discussed in the novelization.
• In Problem Sleuth , there two ways to travel between the real world and the world of imagination: Either climbing through a window, or entering a fort and imagining really hard (booze helps with the latter).
• Homestuck features fenestrated walls. Normally they're used to observe faraway places, but smashing through the wall allows one to travel to the location. Andrew Hussie breaks through one of these walls to get from his house in Real Life to Doc Scratch's house in the trolls' universe. Later, Jade and John use another of these walls to escape a universe that's being written out of existence .
• In Sluggy Freelance Riff invented the Dimensional Flux Agitator (DFA), originally to blast Bun- -bun into a random alternate universe. He and Torg ended up standing on the wrong side and sent themselves instead . He later built a remote allowing people to come back. In theory .
• In Blackbird's Aniverse setting, the hammerspace drive, which can fit in a character's pocket and allows travel into hammerspace , which connects various zones in different dimensions. For example, in the " Kawaii " dimension, there's a Happy Bunny Forest zone, which is an entire universe filled with Exactly What It Says on the Tin . In the "Boring" dimension, there's Tokyo Prime, a universe where Tokyo is the center of everything, but nothing ever happens there, and so on.
• The various dimension-spanning organizations in The Crew of the Copper-Colored Cupids have different means of crossing the barriers between world, but the most common are small ships with traverse the Void on their way to their destination. This includes the Cupids' own vehicles, the Fog Ships, which are stated to be top-of-the-line when it comes to interdimensional vehicle, although that might just be the Cupids' own propaganda.
• Adventure Time: Fionna and Cake : Prismo's remote normally lets him view anything in the multiverse from the Time Room, however he modifies it into a dimension-hopping device and gives it to Fionna. Simon also puts a gem from a destroyed copy of the Ice King's crown in it so that it can take them to universes where the crown exists.
• Family Guy , Stewie invents a remote control that can travel to many universes, including one where Meg is hot, but still ugly compared to everyone else.
• Futurama : Professor Hubert Farnsworth accidentally creates a box that contains another universe where the outcome of every coin flip is reversed. The other universe's Farnsworth created a box containing the main universe. The two Farnsworths wind up creating a ton more of such boxes during the episode.
• On Teenage Mutant Ninja Turtles , the Turtles use the transdimensional portal, a technology that allows travel to alternate universes. It is most commonly used in the 1987 cartoon series. Another approach is used in Turtles Forever ; the Teenage Mutant Ninja Turtles use a dimensional portal stick to go to the 1987 universe.
• W.I.T.C.H. has several magical items that allow travel through dimensions, with the Seal of Phobos (and later the Heart of Kandrakar after it absorbs the seal) being the first example shown, and the Mage's ring and the Tonga Tooth necklace in the second season. Elyon, the Heart of Meridian, can open Folds with her power and jokingly laments that she doesn't get any new jewelry like the others.
• Rick Sanchez of Rick and Morty has a handheld portal gun that shoots out a portal to a dimension of his choosing.
• Star vs. the Forces of Evil : Many characters use dimensional scissors which cut open portals to other universes. They seem to be very common in most dimensions. Star isn't supposed to have any, but her friend Pony Head loans her a pair... which turn out to have been stolen from Hekapoo, the one who forges all dimensional scissors. Marco has to undergo a trial to earn his own pair; it takes him sixteen years to succeed. Even considering the hefty time difference (the trial only took eight minutes from the perspective of everyone else), it's unclear if everyone else who owns a pair of dimensional scissors went through a similar trial.
• Dr. Dimensionpants : The eponymous dimension pants allow the wearer to travel between dimensions.
• What's only known as the Calamity Box from Amphibia transported the protagonist and her two girlfriends to the titular universe where sapient, anthropomorphic amphibians live in a rather dangerous swamp world of monstrous predators. Season 2 has their king reveal that the device was created by his ancestors to traverse various alternate universes, and it needs to be taken to three temples they built to recharge it for another trip. Which is a lie. The Calamity Stones are the actual source of power, and their powers were transferred to the three girls when they first used the box. The temples are actually intended to transfer the power back from the girls to the gems, which the king intends to use to become a Multiversal Conqueror .
• The Owl House has Eda's portal door, which is the only reliable method of passing between Earth and the Demon Realm (the only other way being the Reality Bleeds that cause human junk to wash up on the shores of the Boiling Isles). She mostly uses it to steal human junk to sell at her store , though her posession of it, its history, and how it was made are incredibly important to the show's Myth Arc . The portal gets destroyed in the end, but The Collector has the ability to generate wormholes, and one such wormhole was made between the Boiling Isles and Earth that is stabilized by a new device .

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Dimensional Travel

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What are the best methods of dimensional travel in fiction?

• Thread starter The Vale
• Start date Jan 2, 2020
• Jan 2, 2020

So I saw this "pick a thing" cyoa the other day where every option had some drawback intrinsic to what ti was. One of them was the ability to teleport one way into any fictional universe you know, but you could never go back to one you had already visited and you could never travel to your home universe again. Basically no backtracking with the ability. So that has me wondering - as munchkins do - what are some good alternate travel methods to get around it. Ideally, stop number one would be somewhere you could get a "return home" method, then from there an alternate travel method entirely that would allow you to visit any world you teleport to at will. So, any thoughts on the best means of travelling the multiverse in fiction? As obtainable by your pathetically average human meatsack, that is.  

Malick the last Light

May my light shine bright.

I want to kill the lampreys

The Time Ships in Stephen Baxter's The Time Ships travel back in time to the Big Bang before all timelines diverged, then pick another timeline and go there. They can even pick a timeline where the universe is infinitely big and possesses infinite matter.  

Reality is Overrated

Breachers from the Arrowverse and the Kanohi Olmak, the Mask of Dimensional Gates from Bionicle. Both of them have the power to create portals to any part of the multiverse that they wish to go, and they can do so with naught but a thought.  

Abomination

• Jan 3, 2020

The Continua Device from The Number of the Beast allows instant transit within the universe, to other universes, and to fictional universes. No drawbacks, it doesn't even appear to be power hungry.  

Generalissimo

Generalissimo of spacebattles.

Chronicles of Amber. You just walk to the dimension of your choice. And you can find a target dimension that has any properties you're looking for from local tech level to the local laws of physics.  

evilauthor said: Chronicles of Amber. You just walk to the dimension of your choice. And you can find a target dimension that has any properties you're looking for from local tech level to the local laws of physics. Click to expand... Click to shrink...

The Vale said: As obtainable by your pathetically average human meatsack, that is Click to expand... Click to shrink...

Second mover

Artosh x Riku is otp, des!

Mr Sheldon said: The Time Ships in Stephen Baxter's The Time Ships travel back in time to the Big Bang before all timelines diverged, then pick another timeline and go there. They can even pick a timeline where the universe is infinitely big and possesses infinite matter. Click to expand... Click to shrink...

Avernus said: The Continua Device from The Number of the Beast allows instant transit within the universe, to other universes, and to fictional universes. No drawbacks, it doesn't even appear to be power hungry. Click to expand... Click to shrink...

The weed of Crime bears bitter fruit.

Rick's portal gun from Rick and Morty. Instantaneous, accurate, works basically everywhere, and only seems to need a nebulous 'portal fluid' to function perfectly.  

Second mover said: You guys make it waaay to exclusive. You can just ask your local librarian: L-Space connects all civilized places in the multiverse and is as easy as walking around a bookshelf. Click to expand... Click to shrink...

Avernus said: I thought of that, but there's a problem: If you're a Prince(ss) of Amber or Chaos it's great; if you aren't, then you can't do it. Click to expand... Click to shrink...

Local Phantom Caller

I like that in DBZ they expanded on Instant Transmission with the Kai's (and above) version of Instantaneous Movement. You just can appear anywhere at anytime, no need for locking onto ki signatures like the former. This isn't the coolest or most appealing, but its pragmatically the best I've seen if you need it on a personal use (with the ability to bring aboard as many people who can grab a hold of you).  

Shocker said: Rick's portal gun from Rick and Morty. Instantaneous, accurate, works basically everywhere, and only seems to need a nebulous 'portal fluid' to function perfectly. Click to expand... Click to shrink...

God's Boredom

Every time this pops up I have to recommend a little girl from a short story, Don't Open That Book!. Stella D'Amato has the power that I've always wanted, she can read herself and others into fictional worlds. To return to her own world all she has to do is visualize her bedroom in her mind and like the dude from Jumper, Pop, she instantly teleports to the room she visualizes. That's how her powers work by the way, like the Jumpers, she visualize the places in the stories she reads in her own mind so well that she can just pop into them with a stomach turning distortion of reality. I don't actually recommend the book, it's told from the aunt's point of view and the story is nowhere near as awesome as it sounds, but if you have one shot to go someplace to get something to help you hop dimensions I'd trick Stella into taking me somewhere where I can duplicate her powers, and take the effort to teach her how to use her powers wisely, since I didn't like her fate. For actual easily gotten objects, there's several. The Golden Ticket from Last Action Hero which lets you travel into movies. The magical remotes from Fairly OddParents which let you enter shows playing on the TV. Likewise, Control Freaks remote control which allows the same thing.  

Deadly Serious about Likes

In Yu-Gi-Oh! ARC-V , Reiji gave the Lancers new Duel Disks that has a dimensional warp which is how they're able to get from the Standard Dimension to the Synchro Dimension. That's one best method of dimensional travel.  

Hypochondriac

Sliders. Nothing like not knowing where you are going  

Old walkers are pretty good  

MCU Sling rings are also an excellent method of dimensional travel.  

Pierce the Heavens

hunter 139 said: MCU Sling rings are also an excellent method of dimensional travel. Click to expand... Click to shrink...

Meredith Fayer

The Technodrome has its own dimensional portal. Donatello is able to figure it out in at least one episode, but he's really smart. I doubt a normal human could work the controls to open the portal, but maybe they could get lucky. Next stop: Dimension X!  

Glossary : Dimensional Travel

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Dimensional Travel

The process of leaving the space of our universe and entering that of another one, accomplished by physical, psychic, psionic, or magical means. The mechanics of dimension travel are unknown to all but a few.

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• Published: 28 March 2018

Milestones of low-D quantum magnetism

• Alexander Vasiliev 1 , 2 , 3 ,
• Olga Volkova 1 , 2 , 3 ,
• Elena Zvereva 1 , 2 &
• Maria Markina 1  

npj Quantum Materials volume  3 , Article number:  18 ( 2018 ) Cite this article

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• Magnetic properties and materials
• Quantum mechanics

There is a long time gap between the formulation of the basic theory of low-dimensional (low-D) magnetism as advanced by Ising, Heisenberg and Bethe and its experimental verification. The latter started not long before the discovery of high- T C superconductivity in cuprates and has been boosted by this discovery result in an impressive succession of newly observed physical phenomena. Milestones on this road were the compounds which reached their quantum ground states upon lowering the temperature either gradually or through different instabilities. The gapless and gapped ground states for spin excitations in these compounds are inherent for isolated half-integer spin and integer spin chains, respectively. The same is true for the compounds hosting odd and even leg spin ladders. Some complex oxides of transition metals reach gapped ground state by means of spin-Peierls transition, charge ordering or orbital ordering mechanisms. However, the overwhelming majority of low-dimensional systems arrive to a long-range ordered magnetic state, albeit quite exotic realizations. Under a magnetic field some frustrated magnets stabilize multipolar order, e.g., showing a spin-nematic state in the simplest quadropolar case. Finally, numerous square, triangular, kagome and honeycomb layered lattices, along with Shastry–Sutherland and Nersesyan–Tsvelik patterns constitute the playground to check the basic concepts of two-dimensional magnetism, including resonating valence bond state, Berezinskii–Kosterlitz–Thouless transition and Kitaev model.

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Introduction.

Milestones in the field of low-dimensional magnetism, similar to posts along the road, lead to a very attractive destination, i.e., the formulation of a coherent and unified picture of quantum cooperative phenomena in solids. The story begins in 1925 when Ising following the advice of his tutor Lenz considered infinite chain of magnetic moments with nearest neighbor interaction only. 1 The Hamiltonian considered in this case is valid for the preferred component of the spin S

No spontaneous magnetization at any finite temperature was found within frames of this model. Opposite is the isotropic Heisenberg case 2

The ground states of uniform S  = 1/2 chains are different in these two models. While the chain becomes ordered at zero-temperature in the Ising limit, it remains disordered even at zero-temperature in the Heisenberg limit. In 1931, Bethe introduced his famous “ansatz” method to find the exact quantum ground state of the antiferromagnetic Heisenberg model in one dimension. 3 The extension of classical Ising model to two dimensions was provided by Onsager in 1944. 4 Such a system orders magnetically at finite temperature comparable to the value of exchange interaction parameter J . Two-dimensional Heisenberg system remains disordered at finite temperatures, but its ground state is ordered. The basic role in low dimensional magnetism belongs to Mermin-Wagner theorem formulated in 1966. 5 It states that no one-dimensional or two-dimensional isotropic Heisenberg spin system can order either ferromagnetically or antiferromagnetically at any non-zero temperature.

In the case when the moments lie perpendicular to the chosen axis the model Hamiltonian is

Two dimensional antiferromagnets of XY type form magnetic vortices and antivortices within the plane. The diameters of these objects grow upon cooling. The vortices contact each other at Berezinskii–Kosterlitz–Thouless (BKT) temperature resulting in a unique form of long-range order without spontaneous magnetization. 6 , 7 , 8 An important difference between integer and half-integer spin chains was admitted by Haldane in 1983. 9 The uniform spin-1/2 chain is gapless, it has fractionalized excitations—domain walls carrying spin S  = 1/2. These excitations are confined when chains are coupled into ladders or when there is an alternation of exchange interaction. The uniform spin-1 chain is gapped and the excitations are triplets.

Overall, the properties of magnetic systems depend on their symmetry and dimensionality D . Discrete symmetry (Ising model) can be broken at T  = 0 in D  = 1 and cannot be broken at finite T . Continuous Abelian symmetry (XY model) cannot be broken in D  = 1, but at T  = 0 the correlations decay as power law. In D  = 2 correlations decay as power law at finite T and become exponential above BKT transition. Continuous non-Abelian symmetry SU(2) (Heisenberg model) cannot be broken in D  = 1 even at T  = 0 and can be broken spontaneously only at T  = 0 in D = 2.

The exotic phenomena mentioned in this review are realized in quantum magnets being localized low-spin systems, either spin-1/2 or spin-1, not large classical moments. An attractive feature of some low-dimensional magnets is a spin-liquid state defying a long-range order. The liquid may be either gapped or gapless, dependent on the type of quantum statistics. Adjacent to low-dimensionality is the field of spin frustration, these two phenomena being frequently coexisting in real magnets. The spin-liquid ground state may survive in the presence of strong interaction between magnetic entities, albeit long-range magnetic order establishes itself most frequently in solids upon lowering the temperature due to residual interactions in three dimensions. Numerous attempts were undertaken to find higher-dimensional analogs of the one-dimensional spin−1/2 Heisenberg antiferromagnet (AFM) in a state that breaks neither translational nor spin rotational symmetry. Apart from the isolated ions, the dimers, i.e., two spins coupled by positive (antiferromagnetic) exchange interaction J , seem to be the simplest objects of low-dimensional magnetism. The singlet rotationally invariant ground state of isolated dimers is separated in energy from the triplet excited state by the excitation gap Δ  =  J . The interaction between moments belonging to different dimers, may it be of spin or spin-lattice type, leads to remarkable cooperative phenomena.

The outline of the review is as follows. The 0D objects of quantum low-dimensional magnetism, i.e., spin-1/2 dimers, exhibit a cooperative behavior when coupled. Multiple plateaus appear in magnetization of Shastry–Sutherland dimers network due to the formation of regular patterns of triplet excitations. The plateaus in magnetization can be considered as intermediate Mott insulator phases separating the domes of Bose–Einstein condensation of magnons. Giamarchi, Ruegg and Tchernyshyov underpin the basic concepts of this phenomenon including a detailed correspondence between a Bose gas and a quantum antiferromagnet. 10 Bose–Einstein condensation of magnons is not restricted to spin-1/2 dimers, the representative examples are spin-1 dimers and spin-1 ions with strong anisotropy also.

The chains, either gapped or gapless, represent an evident move from 0D to 1D. The description of uniform and alternating half-integer spin chains is complimented by short detour to integer spin chains. Various phase transitions may bring uniform spin-1/2 chain into ground state with a gap in magnetic excitation spectrum. Among them, spin-Peierls transition, charge ordering and orbital ordering effects can be distinguished. The routine scenario for quasi-one-dimensional system is an eventual 3D order, albeit quite exotic sometimes. Numerous features of this order—chirality, incommensurability, nematicity—make this field of study attractive.

Spin-ladders, to be considered intermediate between 1D and 2D systems, may show either gapped or gapless behavior dependent on leg number. The ladder system can be extended to Nersesyan–Tsvelik network, whose properties are described in some details. As the dimensionality of the system increases, the richer becomes the spectrum of observed magnetic phenomena. It is out of question to list all of them in a short review, but some issues related to 2D square, triangular, kagome and honeycomb lattices are mentioned. The conclusion is supplemented by list of selected spin gap compounds of authors’ choice.

Dimers, Shastry–Sutherland network

A set of orthogonal dimers coupled by frustrated interdimer interaction constitutes the network described by the Shastry–Sutherland model 11 , 12

It is assumed that both intradimer J and interdimer J ′ exchange interactions are positive. Dependent on α  =  J ′/ J ratio, the ground state of this model is either spin singlet ( α  <  α C ) or Neel order ( α  >  α C ), where α C ~0.7.

A good realization of the Shastry–Sutherland model is the SrCu 2 (BO 3 ) 2 . 13 The temperature dependence of the magnetic susceptibility χ in SrCu 2 (BO 3 ) 2 is shown in Fig. 1a . At around T  = 20 K, a steep drop evidences the presence of a spin gap and the singlet/non-magnetic ground state. Evidently, neither the isolated spin dimer model (solid line) nor its mean field modification (dashed line) describes the experimental data. The numerical analysis 12 has shown that the peculiar shape of the χ( T ) curve is due to the fact that the ratio of J  = 100 K and J ′ = 68 K in SrCu 2 (BO 3 ) 2 is quite close to the transition point α C . The almost dispersionless spin gap Δ  = 34 K was evaluated in inelastic neutron scattering. 14

a Temperature dependence of magnetic susceptibility χ =  M / H in SrCu 2 (BO 3 ) 2 taken at μ 0 H  = 1 T (adapted with permission from, ref. 13 copyright American Physical Society 1999). The solid and dashed lines are fitting curves. Inset represents the field dependencies of reduced magnetization M / M sat and its derivative d M /d H taken at T  = 2.1 K for H // c axis (adapted with permission from, ref. 16 copyright American Physical Society 2013). The critical fields H i associated with the plateaus are marked by vertical arrows; b Phase diagram of SrCu 2 (BO 3 ) 2 (adapted with permission from, ref. 19 copyright Springer Nature 2017). Green circles correspond to the triplet gap ∆ at Q  = (2,0, L ), two-triplet bound state (BT) is marked by green diamonds; the dashed line is the extrapolated energy gap and yellow star denotes a new low-energy excitation (LE) at Q  = (1,0,1). Green squares denote magnetic Bragg peaks at Q  = (1,0,0). Magenta line marks the structural transition. Insets represent dimer, plaquette and Neel ground states

Another attractive feature of SrCu 2 (BO 3 ) 2 is the sequence of plateaus in magnetization, as shown in the inset to Fig. 1a . Plateaus are due to the strong localization of the triplet excitations within the set of orthogonal dimers. At the fractions of magnetization, where the triplets create a superstructure, the energy is at a local minimum. At present, the magnetization in SrCu 2 (BO 3 ) 2 investigated in static magnetic fields up to 34 T has revealed the plateaus at 1/8, 2/15, 1/6 and 1/4 of the saturation, 15 while the measurements in pulsed magnetic fields identified additionally 1/3 and 1/2 plateaus. 16 The plateau regions correspond to the spin-gapped states with the stripe order of triplets. It has been argued that the sequence of field-induced phases observed in SrCu 2 (BO 3 ) 2 represents the first example of an incomplete devil’s staircase concerning magnetization of the quantum AFM 15 where the lower plateaus should be described by a superlattice of triplets of the four-Cu spins, instead of dimer triplets. 17

The plaquette phase intermediate between the dimerized spin-singlet state ( α  = 0) and Neel order ( α  → ∞) has been predicted in zero magnetic field for the Shastry–Sutherland network at 0.68 <  α  < 0.86. 18 This phase has been identified recently in inelastic neutron scattering performed on SrCu 2 (BO 3 ) 2 single crystal under pressure up to 60 kbar. 19 As shown in Fig. 1b (left panel), the dimer phase exists up to P  = 16 kbar, where both the gap and the energy of bound triplets decrease. In the range P  = 21.5 ÷ 40 kbar, the new plaquette phase with a spin gap Δ~23 K is identified, as shown in Fig. 1b (middle panel). Eventually, the gap closes under pressure and Neel ordering takes place at P  = 40 kbar. The transition between dimer and plaquette phases is of the first order in the range P  = 16 ÷ 21.5 kbar, while the transition between the plaquette singlet and Neel phase is of the second order. As shown in Fig. 1b (right panel), a further increase in pressure results in a tetragonal monoclinic structural phase transition, where the Cu 2+ spin dimers are no more orthogonal.

Dimers, Bose–Einstein condensation

The ground state energy of a system consisting of integer spin particles, bosons, can be minimized via spontaneous Bose–Einstein condensation (BEC), without any interaction. This phenomenon predicted initially for the photons is considered responsible for superfluidity and superconductivity, refer to condensation of trapped atomic gases and can also be applied to quasiparticles in a solid. 20 Note that the concept of BEC with regard to the spin systems is only an approximation: exchange anisotropy and single-ion anisotropy always break rotational symmetry. Magnons are bosons irrespective of the ions magnetic moment. At low temperatures, the BEC was observed in Heisenberg or axially symmetric low-dimensional magnets with spin-singlet ground state, e.g., spin-1/2 dimers 21 , 22 , 23 , 24 , 25 and composite integer spin chains 26 or in the systems with strong single-ion anisotropy. 27 The BEC occurs under action of magnetic field which splits the triplet S  = 1 and lowers the energy of S z  = 1 level. At the first critical field H C1 , the S  = 0 and S z  = 1 levels cross starting the process of BEC. At low temperatures, the formation of new state is manifested by sharp anomalies in magnetization and specific heat, whose magnitude increases with magnetic field. In the range H C1  <  H  <  H C2 , the canted AFM state exists with net magnetization proportional to the magnetic field. At the second critical field H C2 , the magnetization saturates. In the vicinity of H C1 , the phase boundary for a three-dimensional system should follow the power law H C1 (T)  –  H C1 (0) ~ T 3/2 .

At present, BEC phenomena have been reported at finite temperatures for a number of quantum magnets. 28 Three representative cases are the systems of spin-1/2 dimers, spin-1 dimers and isolated S  = 1 ions. The ancient Han purple pigment, BaCuSi 2 O 6 , is a spin gap compound with a square lattice of dimers forming the bilayer structure. 23 Along the c axis, the Cu 2+ ions, S  = 1/2, are coupled by J  = Δ = 52 K. In addition, these ions are coupled in the ab plane by J ′ = 7 K. The BEC critical fields in BaCuSi 2 O 6 are μ 0 H C1  = 23.5 T and μ 0 H C2  = 49 T with T max  = 3.8 K. The dome shaped phase boundary of the ordered phase in BaCuSi 2 O 6 is shown in Fig. 2a . This boundary is marked by sharp anomalies in specific heat and magnetocaloric effect.

The phase diagrams of BEC. Symbols represent the data of specific heat and magnetocaloric (MC) measurements. a BaCuSi 2 O 6 , experimental (solid) and calculated (dash) magnetization curves at 1.5 K for H // c axis (lines), Δ T refers to MC effect (adapted with permission from, ref. 23 copyright American Physical Society 2009); b Ba 3 Mn 2 O 8 , the phases I and III are marked as measured for H // c axis, phase II appears at H // a axis (reproduced with permission from, ref. 25 copyright American Physical Society 2009); c NiCl 2 -4SC(NH 2 ) 2 , the inset depicts the crystal structure (adapted with permission from, ref. 27 copyright American Physical Society 2006)

The singlet−triplet and triplet−quintuplet BEC was studied in the spin-1 dimer compound, Ba 3 Mn 2 O 8 . 25 Its magnetic subsystem is comprised of pairs of Mn 5+ ions arranged on triangular lattice and coupled along the c axis by J  = 19 K. The multiple interactions between dimers amount to J ′ ~1 K, while the single-ion uniaxial anisotropy is D ~0.3 K. The ground state of S  = 1 dimers is the singlet; the first excited state is the triplet S  = 1 (Δ 1  =  J ); and the second one is the quintuplet S  = 2 (Δ 2  = 3  J ). Under magnetic field both excited states split and levels S z  = 1 and later S z  = 2 cross the ground state level. The field dependence of magnetization of Ba 3 Mn 2 O 8 demonstrates two linear regions corresponding to BEC, as shown in Fig. 2b . At T  = 0.5 K, the critical fields for triplet BEC are μ 0 H C1  = 8.73 T and μ 0 H C2  = 26.46 T with T max1  = 0.86 K, while for the quintuplet BEC μ 0 H C3  = 32,42 T and μ 0 H C4  = 47.9 T with T max2  = 0.63 K. The magnetization plateau in the range μ 0 H C2 –μ 0 H C3 corresponds to one S = 1 triplet per dimer. Two dome-shaped phase diagram in Ba 3 Mn 2 O 8 for field perpendicular to the c axis is shown in Fig. 2b . The regions I and II correspond to different phases of the triplet condensate; the region III corresponds to the quintuplet condensate. 29

A qualitatively different case of BEC is represented by NiCl 2 -4SC(NH 2 ) 2 (DTN), where the gap between singlet S  = 0 and doublet S z  = ±1 levels is due to a single-ion anisotropy D  = Δ = 8 K of isolated S  = 1 Ni 2+ ions. 27 In this compound, the nickel ions are surrounded by four polar molecules of thiourea, making the DTN a molecular magnet. Similar to dimers, an external magnetic field shifts down the S z  = 1 level. The critical fields in DTN are μ 0 H C1  = 2 T and μ 0 H C2  = 12.5 T with T max  = 1.2 K (Fig. 2c ). In variance with the dimer systems where the gap is basically isotropic, the properties of DTN strongly depend upon the direction of the magnetic field with respect to the easy magnetization axis.

Chains, spin liquids

The uniform half-integer spin chain does not present a gap in the triplet excitation spectrum. The chain is disordered in an isotropic case but the anisotropy of exchange interaction results in a long-range order at T  = 0 K. 30 The system with small exchange anisotropy can be described by the pure Heisenberg form JS i S j while the Ising form JS i z S j z should be applied to the highly anisotropic case. 31 The χ( T ) curve of Heisenberg AFM spin-1/2 chain demonstrates a broad maximum at T max ~0.64  J . Below this temperature, it is reduced by ~15%. At the same time, the Ising chain demonstrates a broad maximum in χ( T ) curve at T max  = 0.5  J and its reduction to zero at T  = 0 K. There are many good examples of uniform Heisenberg spin-1/2 chains, among them AE 2 Cu(PO 4 ) 2 (AE = Sr, Ba). 32 The broad maxima in χ( T ) curves are seen at T max  = 92 K ( J  = 143 K) for the Sr- and T max  = 82 K ( J  = 132 K) for the Ba-compounds (Fig. 3a ). Although the Sr 2 Cu(PO 4 ) 2 seems to be the best realization of a Heisenberg spin-1/2 chain, 33 the measurements of ac –susceptibility identified the long-range order in the Sr-compound at T N  = 0.085 K. 34

Temperature dependencies of magnetic susceptibility χ in spin chain systems. a gapless uniform spin-1/2 chains in Sr 2 Cu(PO 4 ) 2 and Ba 2 CuP 2 O 8 (adapted with permission from, ref. 33 copyright American Physical Society 2006); b gapped alternating spin-1/2 chain in BaCu 2 V 2 O 8 (adapted with permission from, ref. 39 copyright American Physical Society 2004), the dotted line is an extrapolation of impurities term; c gapped uniform spin-1 chain in PbNi 2 V 2 O 8 (adapted with permission from, ref. 47 copyright American Physical Society 1999). The fragments of crystal structures are depicted in the insets in each panel

An alternation of the exchange interaction along the spin-1/2 chain, J 1 – J 2 , leads to the appearance of a spin gap in the excitation spectrum. The confined excitations carry spin 0 and 1, the gap for triplet excitations is located at q  = π. 35 Depending on the alternation parameter 0 ≤  α  =  J 2 / J 1  ≤ 1 two limiting cases can be considered. For α  = 0, the chain transforms into a set of isolated dimers; for α  = 1, it is the uniform chain. In the range 0 ≤  α  ≤ 0.9, the spin gap is defined as Δ =  J 1 (1 −  α ) 3/4 (1 +  α ) 1/4 . 36 In the case of ferromagnetic (FM) exchange interaction J 2 alternating with AFM J 1 , the energy spectrum is gapped also. The gap is located at q  =  π /2 similar to the AFM Heisenberg S  = 1 chain. 37 The χ( T ) curves show the correlation maximum, which shifts from T max ~0.64 J 1 at α  = | J 2 |/ J 1  = 0 to lower temperatures with α increasing. 38 An alternating spin-1/2 chain compound with a large spin gap is BaCu 2 V 2 O 8 . 39 The χ( T ) curve demonstrates a broad maximum at T max  ≈ 280 K (Fig. 3b ) which enables estimation of a leading exchange interaction as J 1  = 460 K. The spin gap found in 51 V NMR measurements amounts to 380 K. 40 While first principles calculations identified BaCu 2 V 2 O 8 as an AFM–AFM chain compound with α equal to either 0.16 (Ref. 41 ) or 0.05 (Ref. 42 ), recent high-resolution inelastic neutron scattering data unveiled an AFM–FM alternating chain with J 1  = 475 K and J 2  = −140 K. 43

Integer spin chains with sufficiently weak anisotropy are characterized by a nonmagnetic singlet ground state and a nonzero excitation-energy gap. 44 Hamiltonian of spin-1 chain is

where λ is the exchange interaction anisotropy and μ is the crystal field splitting of the single ion levels. The gapped phase exists in an extended range of exchange anisotropy 0 ≤  λ  ≤ 1.18 for μ  = 0. 45 Moreover, for λ  ≈ 1, the gap decreases, goes through a minimum, estimated to be zero, and then increases with positive μ . Monte Carlo calculations performed for spin-1 AFM Heisenberg chain estimate the gap Δ = 0.41  J . 46 PbNi 2 V 2 O 8 is considered to be an example of the Haldane chain conjecture. The χ( T ) curve evidences the presence of the gap in the energy spectrum (Fig. 3c ). The position of the broad maximum at T max  = 120 K allows estimating J  = 95 K and Δ = 39 K. 47 However, the determination of the spin gap from magnetization curves gives a lower value Δ = (2Δ ⊥  + Δ || )/3 = 22 K. This is ascribed to the presence of both interchain interactions J ⊥ and negative single ion anisotropy D . In inelastic neutron scattering the main magnetic parameters in PbNi 2 V 2 O 8 were estimated as J  = 110 K, J ⊥  = 1 K and D  = −2.7 K. The values of transverse and longitudinal gaps constituted Δ ⊥  = 48 K and Δ ||  = 43 K. 48 The D / J and J ⊥ / J ratios put Pb 2 Ni 2 V 2 O 8 system in the Haldane phase near the border with the ordered Ising-like phase in the D - J ⊥ phase diagram. 46

Chains, phase transitions, spin gap

The uniform spin-1/2 chains are unstable with respect to various effects leading to a spin gap formation. The interactions of spin, charge and orbital degrees of freedom with the lattice lead to the spin-Peierls transition, charge and orbital order driven transitions. All of them include structural distortion and in every case a loss in elastic energy is compensated by a gain in magnetic energy.

The spin-Peierls transition, being the most unusual kind of magnetoelastic transition, relates to the particular quantum mechanical nature of quasi-one-dimensional AFM. Similar to the Peierls transition in quasi-one-dimensional conductors, the spin-Peierls transition integrates spin gap formation and dimerization of the underlying crystal lattice. This phenomenon, found initially in tetrathiafulvalene-CuS 4 C 4 (CF 3 ) 4 at T SP  = 12 K, 49 was observed later in CuGeO 3 . 50 In contrast to the AFM transition, the reduction of magnetic susceptibility χ at the spin-Peierls transition is isotropic. This is illustrated by χ( T ) curves measured along three principal axes in CuGeO 3 (Fig. 4a ). The broad correlation maximum is reached at T max  = 56 K, which defines the intrachain exchange interaction along the c axis J  = 88 K. The spin-Peierls transition is manifested by a sharp drop in the χ( T ) curve at T SP  = 14 K. Under magnetic field, the transition shifts to lower temperatures ~ αH 2 with α  = 0.46. 51 At T  <  T SP , two alternating J ’s form, i.e., J 1,2 ( T ) =  J (1±δ( T )). The spin gap Δ = 24 K is proportional to the alternation δ  = 0.17. The values of interchain exchange interactions along the b axis J b  = 0.1  J and c axis J c  = −0.01  J were provided by inelastic neutron scattering. 52 All spin-Peierls compounds obey universal magnetic phase diagram comprised of uniform, dimerized and intermediate phases. 53 The last one is considered to be a commensurate, discommensurate (a magnetic soliton), or incommensurate phase. The critical field of the transition between dimerized and intermediate phases in CuGeO 3 is 12-13 T. 54 Full saturation of magnetization in CuGeO 3 was achieved at μ 0 H  = 253 T in pulsed magnetic field measurements. 55

a The spin-Peierls transition in CuGeO 3 (adapted with permission from, ref. 50 copyright American Physical Society 1993). Symbols represent the experimental data taken along three principal axes; b The charge ordering transition in NaV 2 O 5 (adapted with permission from, ref. 56 copyright Physical Society of Japan 1996). c The orbital ordering transition in NaTiSi 2 O 6 (adapted with permission from, ref. 61 copyright Physical Society of Japan 2002). The solid lines in b and c represent the Bonner–Fisher curve. The dashed line in panel c represents the Curie–Weiss law. All measurements were taken at μ 0 H  = 1 T. The fragments of crystal structures are depicted in the insets in each panel

A charge-ordering-driven phase transition into the spin gap state was observed in the NaV 2 O 5 at T C  = 35 K (Fig. 4b ). 56 At elevated temperatures, the average oxidation state of vanadium ions is V 4.5+ . Below T C , two distinctly different oxidation states were evidenced in V 51 NMR measurements which also identified a spin gap value Δ = 108 K. 57 At low temperatures, the monoclinic A 112 structure of NaV 2 O 5 is constituted by enlarged unit cell ( a - b ) × 2 b  × 4 c , where a , b and c are the crystal lattice parameters of the high-temperature orthorhombic phase. 58 At T  ≤  T C , the temperature-dependent charge disproportionation V 4.5±δc/2 was observed with continuous variation of δ c . 59 The fully charged zigzag-type pattern differs distinctly from the chain-type considered a prerequisite to the spin-Peierls state. At present, the alternation of exchange interaction within zigzag chain is considered to be responsible for a spin gap. The low temperature crystal structure in NaV 2 O 5 is fixed by both lattice distortion and Coulomb repulsion. These two factors are responsible also for the “devil’s staircase” phase transitions between commensurate phases with 2 a ×2 b ×z c type superstructures found in NaV 2 O 5 . 60

A spin-Peierls-like phase transition 61 driven by spin-orbital fluctuations 62 was observed in NaTiSi 2 O 6 . The transition takes place at T C  = 210 K which is higher than the temperature of correlation maximum in χ( T ) curve. 31 In this case, the short-range order within the chains is not fully developed and solely magnetic fluctuations cannot be considered to be the driving force. NaTiSi 2 O 6 hosts the skew-edge-sharing chain of slightly distorted TiO 6 octahedra in monoclinic C 2/ c structure. 63 At elevated temperatures, the fluctuations of the orbital degrees of freedom allow NaTiSi 2 O 6 to be considered as a dynamic Jahn−Teller phase. 64 At T C  = 210 K, NaTiSi 2 O 6 transforms to triclinic \(P\bar 1\) modification 63 which is accompanied by a gradual decrease in magnetic susceptibility (Fig. 4c ). The exchange interaction J along the chain is provided by the overlap of nearly degenerated \(\left| {xy} \right\rangle\) and \(\left| {yz} \right\rangle\) orbitals ( \(\left| {xz} \right\rangle\) orbitals are non-bonding). Taking into consideration the orbital degree of freedom, the Hamiltonian of this system can be written as 64

where the orbital operator \(T_i^z\)  = 1/2 corresponds to an occupied \(\left| {xy} \right\rangle\) orbital and \(T_i^z\)  = −1/2 to an occupied \(\left| {yz} \right\rangle\) orbital. The ground state of this Hamitonian is a dimerized orbital-ordered one hosting the spin singlet on each bond. The states with either \(\left| {xy} \right\rangle\) or \(\left| {yz} \right\rangle\) occupied are degenerated. The condensation of the system in either one of these states explains the appearance of a large singlet-triplet spin gap. The value of gap Δ = 620 K was estimated in time-of-flight neutron spectroscopy 65 in good correspondence with the first principles calculations. 66

Chains, phase transitions, long-range order

The long-range order is the final destination for numerous quasi-one-dimensional magnets not protected by a spin gap. This is because the weak interchain exchange interactions J ′ inevitably come into play upon lowering the temperature. The ground state of these systems also depends on both signs and values of nearest neighbor J nn and next nearest neighbor couplings J nnn within the chains. 67 The chain Hamiltonian in a magnetic field H is

In the case of J nnn being antiferromagnetic ( J nnn  > 0), the chain is frustrated independent of the sign of J nn . If both J nn and J nnn are positive, a spin gap opens at J nnn / J nn  =  α  >  α C  = 0.241. 68 At α  = 0.5, the Majumdar–Ghosh ground state is represented by a superposition of spin singlets. Tentatively, copper chromate, CuCrO 4 , is the best realization of this model with J nn  = 54 K and J nnn  = 27 K. 69 It should be noted, however, that no spin gap was observed experimentally in the compounds which satisfy the criterion α  >  α C . If J nn is FM ( J nn  < 0), FM order within the chain is established in the range −0.25 <  α  ≤ 0. At α  = −0.25, the system undergoes quantum phase transition to an incommensurate spin helix state. 70 Among recently found species of this type there are several chain cuprates, e.g., LiCu 2 O 2 , 71 Li 2 CuZrO 4 , 72 LiCuSbO 4 , 73 etc., which adopt non-collinear magnetic structure. Of special interest is LiCuVO 4 which exhibits ferroelectricity at low temperatures and nematicity at high magnetic fields.

In LiCuVO 4 , the Cu 2+ ions form isolated spin-1/2 chains along the orthorhombic b axis. 74 The signs of the exchange interactions within the chains differ, i.e., J nn  = −19 K while J nnn  = 44 K. The long-range helix order at T N  = 2.4 K is triggered by the interchain interaction J′  = −4.6 K. 75 The ordered moments of Cu 2+ ions form a spiral spin ground state in the ab plane with incommensurate propagation vector Q  = (0;0.532;0). LiCuVO 4 is an improper ferroelectric with the long-range polar order induced at the onset of a spiral spin order. Measurements of magnetic-field-dependent dielectric constant ε and electrical polarization P allow the construction of a magnetoelectric phase diagram (Fig. 5a ). 76 At T  <  T N and H  <  H 1 ~2.5 T, the normal vector e to ( a , b ) helix in LiCuVO 4 is parallel to the c axis. At a critical field H 1 ~2.5 T, the vector e is turned into the direction of the external field. According to the symmetry rule of spiral magnets, ferroelectric order is established with the polarization P   ∝   e   ×   Q along the a axis. In the range H 1  <  H  < H 2 ~7.5 T, the normal vector e reorients along the external magnetic field and, thus, the electrical polarization depends on the direction of the magnetic field. Finally, for external magnetic fields above H 2 , the helical spin structure is destroyed and the system is paraelectric for all field directions.

a ( H , T ) phase diagram of LiCuVO 4 (adapted with permission from, ref. 76 copyright American Physical Society 2008). The magnetic and electric states are noted in the figure; b 51 V NMR spectra in LiCuVO 4 for H ∥ b (reproduced with permission from, ref. 78 copyright American Physical Society 2017). The peak of each line is marked by the black triangle. Spin-density wave, spin nematic and saturated field ranges are highlighted by different colors. The dash-dotted lines denote field-dependent H int ; c ( H , T ) phase diagram of LiCuSbO 4 (adapted with permission from, ref. 79 copyright Springer Nature 2017). The dark red area corresponds to an anomalous spin density wave phase; the dark yellow area depicts a nematic phase. The blue line marks the isosbestic field H c1 . The brown circles depict the maximum of the spin-nematic correlation function H SN max

Above H 2 , an incommensurate, collinear spin density wave of bound magnon pairs is stabilized in medium magnetic fields by a FM J nn . In high fields just below the saturation of magnetization, these pairs experience a Bose–Einstein condensation into quantum multipolar states. One of these states expected just below the saturation H S is a quadrupolar state of magnon pairs called a spin nematic state, analogous to a nematic liquid crystal. In a spin nematic state, an energy gap develops in the transverse spin-excitation spectrum making the energy of the two-magnon bound state lower than the energy of the single-magnon state. 77

The microscopic experimental evidence for the formation of a homogeneous, field-dependent, longitudinal spin state without transverse dipolar order was obtained in nuclear magnetic resonance (NMR) measurements on LiCuVO 4 single crystals up to 56 T for both H ∥ c and H ∥ b orientations. 78 Observed was the field-dependent NMR line position without change of its width with respect to the saturated phase, as predicted for a spin nematic phase. Figure 5b shows the field dependencies of the 51 V spectra for H ∥ b taken at T  = 1.3 K. The internal local field H int generated on 51 V by the transferred hyperfine coupling from the neighboring Cu 2+ moments directly measures the local magnetization M , and is thus extracted using H int  = ν( 51 V)/ 51 γ − μ 0 H where ν is the frequency and γ is the gyromagnetic ratio.

Three different regions can be identified in these NMR spectra. At H  > 50.55 T (43.55 T for H ∥ c ), the spectra are field independent and consist of narrow and symmetric lines which is characteristic for a saturated homogeneous magnetic phase. At H  < 48.95 T (42.41 T for H ∥ c ) there appears a strong line broadening; both linewidth and line position are field dependent, which is consistent with the previously identified spin density wave state. This phase is characterized by a modulated spin polarization, where the moments are collinear with the external field. In the field ranges 48.95÷50.55 T for H ∥ b (42.41÷43.55 T for H ∥ c ), the line positions change with H as in the spin density waves phase, but their widths remain unchanged relative to those of the saturated phase. This behavior corresponds to the formation of a homogeneous magnetic state as expected for a spin-nematic state.

In variance with LiCuVO 4 , its newly synthesized counterpart LiCuSbO 4 does not exhibit long-range order down to 0.1 K, signifying the weakness or frustration of interchain exchange interactions. Indications on the presence of a field-induced spin-nematic state were obtained in measurements of temperature dependencies of 7 Li nuclear spin lattice relaxation rate, T 1 −1 , at various fields. 79 Below threshold field μ 0 H c1  = 13 T, T 1 −1 diverges at lowering temperature pointing to approach of magnetically ordered phase. Surprisingly, above this field T 1 −1 shows drastic suppression of relaxation rate at lowering temperature evidencing a gap in magnetic excitation spectrum. Excluding well established mechanisms for the spin gap formation, i.e., Zeeman effect at saturation magnetization and Dzyaloshinskii-Moriya interaction, it was concluded that an external magnetic field induces a multicomponent spin liquid in LiCuSbO 4 . According to phase diagram, shown in Fig. 5c , a collinear incommensurate spin density wave phase precedes spin-nematic phase, both being gapped. The range of possible multipolar nematic phase was narrowed to 12.5–13 T, recently. 80 Thus, the study of LiCuSbO 4 gives further support to the concept that the fragile multipolar phases may survive in low-dimensional magnets due to enhancement of quantum fluctuations in the presence of competing and strongly anisotropic exchange interactions.

Ladders, Nersesyan–Tsvelik network

Isolated magnetic entities consisting of exchange-coupled chains constitute the multitude of spin ladders. 81 The magnetic excitation spectra are gapped for half-integer even leg ladders and gapless for odd leg ladders. In the former case the fractionalized spin -1/2 excitations are confined so that the excitations carry spin 0 and 1. Depending on the ratio of the rung J r and the leg J l exchange interactions, various ground states could be formed in these objects. In the case of J r ≫ J l , the even leg ladder can be considered as the collection of weakly interacting dimers. In the opposite case of J r ≪ J l , independent on the number of legs, the pattern is that of weakly interacting gapless chains. In the case of the spin-1 ladder the ground state is gapped for any ratio of J r and J l . Of special interest is the Nersesyan–Tsvelik network, which is an extension of the spin-ladder pattern to the layer where both rung J r and plaquette-diagonal J d exchange interaction are taken into account. 82

In the coupled chains model the spin liquid state of the two-dimensional counterpart of one-dimensional spin-1/2 Heisenberg AFM can be realized when the exchange is frustrated in the direction perpendicular to the chains and can be fine-tuned. In the case for which the interchain couplings satisfy the relation J r  = 2 J d , the interaction between staggered magnetizations is eliminated completely. Both frustration and spatial anisotropy of exchange interactions are essential ingredients of the Nersesyan–Tsvelik model. The Hamiltonian in this case is

where S j,n are spin-1/2 operators, J l , J r , J d  > 0 and J l ≫ J r , J d .

The spatially anisotropic square lattice quantum AFM was analyzed by Starykh and Balents who showed that to realize the Nersesyan–Tsvelik model just the reduction of the coupling of staggered magnetization of different chains is needed, not full elimination. 83 An attempt to verify this model involves the (NO)Cu(NO 3 ) 3 . The layered crystal structure of this compound is organized by weakly coupled chains running along the b axis, as shown in Fig. 6a . 84 The intrachain exchange interaction, J l , passes through NO 3 − group which bounds neighboring Cu 2+ ( S  = 1/2) ions. Within the bc plane these ions are coupled by rung exchange interaction, J r , involving two NO + groups and diagonal exchange interaction, J d , which passes through one NO + group. It allows presuming that J r  = 2 J d . The interplane exchange interaction along the a axis is considered to be small.

a Nersesyan–Tsvelik pattern in (NO)Cu(NO 3 ) 3 (adapted with permission from, ref. 84 copyright American Physical Society 2010). Arcs denote main exchange interactions between Cu 2+ ions; b magnetic Raman scattering with a finite energy maximum (adapted with permission from, ref. 85 copyright American Physical Society 2012); c inelastic neutron scattering data of spinon continuum at 5.5 K (adapted with permission from, ref. 86 copyright American Physical Society 2014); d simulation of spinon continuum with J  = 142 K. The boundary of two-spinon continuum is marked by dashed line (adapted with permission from, ref. 86 copyright American Physical Society 2014)

The temperature dependencies of both magnetic susceptibility χ and electron spin resonance intensity χ ESR in (NO)Cu(NO 3 ) 3 have been described by the formalism appropriate for isolated half-integer spin chains with J l  = 170 K. However, the value of χ at low temperatures was found to be significantly smaller than expected for an isolated spin-1/2 Heisenberg chain. Another probe of the spin liquid state was Raman spectroscopy which evidenced a gapless continuum of magnetic origin (Fig. 6b ). 85 The position of the maximum in this continuum defines the major exchange coupling along the chains as J l  = 150 K. That same spinon continuum was observed in inelastic neutron scattering (Fig. 6c ). 86

The condition J r  = 2 J d requires a subtle fine tuning of the couplings. The deviation from this ratio may lead to formation of the Neel state at low temperatures. In the band structure calculations, it was admitted that J r  = 2 J d ratio may not be fulfilled in (NO)Cu(NO 3 ) 3 because the interaction between NO 3 − units flared out of the plane of Fig. 6c may contribute to J r but may not contribute to J d . 87 Indeed, the long-range magnetic order occurs at the highly reduced Neel temperature T N  = 0.58(5)K. 86 The large ratio J l / T N ~ 2.5 × 10 2 marks the strong suppression of magnetic order. Furthermore, the specific heat C p and muon spectroscopy (μSR) imply a small ordered moment m while the neutron diffraction gives an upper limit of m ~0.01 μ B . Evidence that the interchain interactions are competing comes from μSR, which shows that the magnetic order is an incommensurate spin density wave. Since the inelastic neutron scattering reveals commensurate magnetism along the chains, the order must be incommensurate perpendicular to the chains. Hence, the (NO)Cu(NO 3 ) 3 can be considered as a highly one-dimensional chain compound with frustrated interchain interactions. Tentatively, it corresponds to the Nersesyan−Tsvelik model with finite and competing values of J r and J d , although the ratio of these interactions and the proximity of the system to the special point J r  = 2 J d is still unknown.

Layers, triangular, kagome and honeycomb lattices

The interest to layered magnets has been triggered by discovery of superconductivity in La 2   -   x Ba x CuO 4 which possesses a square layered magnetic lattice. 88 The issue of quantum ground state in such a lattice belongs to the most complicated ones since the competition of intralayer exchange interactions along with interlayer interactions and anisotropy may significantly influence the long-range ordering processes. The introduction of holes into the copper layers leads to frustration of magnetic interactions and formation of resonating dimer singlets, i.e., mobile Cooper pairs. This allowed Anderson advance a concept of high-T C superconductivity in cuprates based on idea of resonating valence bond (RVB) state. 89 Such a quantum spin liquid state was suggested initially to describe valence bond interactions in geometrically frustrated 2D system of Mott insulator. 90 To realize the spin liquid state in two dimensions the most obvious candidates are triangular and kagome lattices.

Among triangular 2D spin-1/2 Heisenberg antiferromagnets, Cs 2 CuCl 4 is considered to be a closest realization of a quantum spin liquid. 91 Within planes of this compound the copper spins form an anisotropic frustrated network with linear chain coupling J along the b axis and zigzag inter-chain coupling J ′ ~ J /3 along the c axis, as shown in the inset to Fig. 7b . Present are also order of magnitude smaller inter-plane coupling J ′′ and in-plane Dzyaloshinskii–Moriya term D responsible for incommensurate spiral order at T N  = 0.62(1)K. 92 A distinctive feature of Cs 2 CuCl 4 revealed by inelastic neutron scattering is the presence of highly dispersive excitation continuum indicative of fractionalization of S  = 1 spin waves into pairs of deconfined S  = 1/2 spinons, as shown in Fig. 7a . Below T N , the sharp excitations appear at low energies, but the dominant continuum at higher energies remains basically unchanged. It was argued by Kohno, Starykh and Balents, 93 that the sharp excitations represent the spinon bound states, i.e., triplons, rather than magnons which are modes of a long-range ordered magnet. The data obtained suggest that Cs 2 CuCl 4 could be placed into close proximity to quantum critical point separating fractional resonating-valence-bond (RVB) spin liquid and a magnetically ordered state, as shown in Fig. 7b . In a magnetic field, the phase diagram of Cs 2 CuCl 4 has been found to be quite sensitive to smallest interactions. 94 These interactions may induce entirely new phases and are responsible for commensurate-incommensurate transition. A cascade of energy scales pertinent to Cs 2 CuCl 4 in a magnetic field oriented along the b axis is represented by Fig. 7c .

a Dynamical structure factor for dispersion relations at k y ′ = 0 (left), k y ′ = 2 π (center) and k y ′ = 3 π (right) in Cs 2 CuCl 4 . (adapted with permission from, ref. 93 copyright Springer Nature 2007, and, ref. 91 copyright American Physical Society 2001). b Phase diagram of a quasi-2D frustrated quantum magnet with deconfined spinons near an instability to spiral long-range order driven by a small parameter P in the Hamiltonian (such as the interlayer coupling) (adapted with permission from, ref. 92 copyright American Physical Society 2003). c The schematic cascade of energy scales relevant to Cs 2 CuCl 4 , which is to be considered from largest to smallest (reproduced with permission from, ref. 94 copyright American Physical Society 2010)

Quite a few 2D compounds were considered hosting a quantum spin liquid on a geometrically frustrated kagome lattice. Among them, volborthite 95 Cu 3 V 2 O 7 (OH) 2  × 2H 2 O, vesignieite 96 BaCu 3 V 2 O 8 (OH) 2 and herbertsmithite 97 ZnCu 3 (OH) 6 Cl 2 , the last one being a subject of strictest scrutiny. The main copper–copper antiferromagnetic exchange parameter within network of corner-sharing triangles in ZnCu 3 (OH) 6 Cl 2 was estimated as J ~200 K from the slope of χ( T ) curve at T  > 200 K, but no evidence on long-range order was obtained down to 50 mK. 98 A peculiar feature of herbertsmithite masking its ground properties is an inevitable partial substitution of inter-plane Zn 2+ by Cu 2+ . These defects largely define the low temperature magnetic susceptibility χ of ZnCu 3 (OH) 6 Cl 2 . To reveal the intrinsic properties of a kagome layer much better is the local probe, i.e., 17 O NMR lineshift. 99 Temperature dependence of this property is markedly different from that of a bulk probe. While the χ( T ) dependence resembles the Curie law, 17 O NMR lineshift passes through broad maximum at elevated temperatures and becomes temperature-independent at lowest temperatures. The fractional spin excitations in ZnCu 3 (OH) 6 Cl 2 form flat continuum evidenced in neutron scattering measurements. This is a signature of a quantum spin liquid. The key issue in this respect is the presence (or absence) of a spin gap. While it was not established unambiguously, the neutron scattering data set an upper limit for the spin gap value of about 0.1  J , if any. 100 Evidence for a gapped spin-liquid ground state was obtained from the 17 O NMR lineshift measurements on herbertsmithite single crystal. It was demonstrated that the intrinsic local susceptibility of kagome lattice tends to zero at T  < 0.03  J . 101 These experimental data are crucial to distinguish between various theories on quantum ground state of spin-1/2 Heisenberg AFM on a kagome lattice, including valence-bond solid, gapped and gapless spin liquids.

Among quantum theoretical models of two-dimensional magnets an important role belongs to the Kitaev model where an exact solution for a spin-1/2 honeycomb lattice with anisotropic bond-dependent interactions exists. 102 The ground state in the pure Kitaev model is a quantum spin liquid, either gapped or gapless depending on the exchange interaction parameters (Fig. 8a ). Beyond the pure Kitaev limit, four other types of the ground state can be realized in honeycomb lattice dependent on anisotropy and frustration triggered by competition of exchange interactions: FM, Neel’s AFM, AFM zigzag and AFM stripe order (Fig. 8b ).

a Kitaev spin liquid with bond anisotropy (reproduced with permission from, ref. 114 copyright American Physical Society 2014); b magnetic phases captured by the bond-anisotropic Kitaev−Heisenberg model (reproduced with permission from, ref. 114 copyright American Physical Society 2014); c experimental evidence for proximity to the Kitaev quantum spin liquid (QSL): magnetic heat capacity C mag and magnetic entropy S mag in units of R ln2 vs T for Na 2 IrO 3 . The dash-dotted line corresponds to 1/2 R ln2 (reproduced with permission from, ref. 107 copyright American Physical Society 2017); d color plot of the data at T  = 5 K with the magnetic modes ( M 1 and M 2) detected in inelastic neutron scattering at E  = 4 and 6 meV. M 1 shows a minimum near Q  = 0.62 Å -1 , close to the M point of the honeycomb reciprocal lattice. The arrow shows the concavity of the M 1 mode (adapted with permission from, ref. 108 copyright Springer Nature 2016); e structure and polarized Raman response of α-RuCl 3 at 5 K. The shaded blue region indicates the continuum contribution (adapted with permission from, ref. 110 copyright American Physical Society 2015)

The Kitaev model has generated a new trend in the study of quantum spin liquids due to the topological nature of its solution: in contrast to conventionally ordered magnets, which possess bosonic elementary excitations (magnons), in such a state spins S  = 1/2 are predicted to fractionalize into itinerant Majorana fermions and localized Z 2 fluxes. 103 , 104 , 105 The quantum liquid state preserves all the symmetries of the high-temperature paramagnet even at T  = 0 K and evade a description by conventional local order parameters, because the fractionalization affects both thermal and dynamic properties of these topological phases. The signatures of the Kitaev spin liquid are (i) two peaks at T l and T h in specific heat curves, C p ( T ), caused by the fractionalization of spins; (ii) a plateau at 1/2 R ln2 in C p ( T ) curves in between these peaks; (iii) incoherent spectra of dynamical spin structure factors S (q,ω), iv) small ratio T l / T h  ≤ 0.03. 106

The most popular candidates for the experimental verification of the Kitaev model have been limited up to now to spin-1/2 systems with 5 d and 6 d elements, and most importantly A 2 IrO 3 ( A  = Li,Na) and α−RuCl 3 . Strong spin-orbit coupling was found to play a key role in the formation of anisotropic bond-dependent interactions on the honeycomb lattice in this case. Despite expectations, however, all these compounds do not have a true spin-liquid ground state because they demonstrate long-range AFM order at low temperatures, preceded by a wide maximum on the temperature dependence of the magnetic susceptibility. This cannot be related to Kitaev interactions, originating from the direct exchange between the transition metal ions. At the same time, the properties of these compounds at elevated temperatures reflect the proximity to Kitaev model and remain to be of great interest.

For instance, two peaks in the C p ( T ) caused by the fractionalization of spin to two types of Majorana fermions and plateau/shoulder pinned at 1/2 R ln2 in S mag ( T ) have been observed recently for Na 2 IrO 3 , as shown in Fig. 8c . 107 Fractionalized elementary excitations, reflecting the peculiarity of quantum spin liquid, have been identified in inelastic neutron scattering where they constitute a continuum, sharply distinct from the magnon modes inherent for ordered magnets. Such incoherent spectra were observed in inelastic neutron scattering 108 , 109 (Fig. 8d ) and Raman experiments (Fig. 8e ) in α−RuCl 3 . 110 , 111

The BKT paradigm formulated initially for the frustrated square lattice can be extended to triangular, kagome and honeycomb systems also. This concept presumes a phase transition from unbound vortex and antivortex state of two-dimensional magnet to the coupled vortex–antivortex phase at low temperatures. Below critical temperature of this transition, the formation of topological defects (vortex-antivortex pairs) leads to the appearance of additional degree of freedom, i.e., chirality.

The versatile phenomena seen in low-D quantum magnets are just mentioned here in an introductory manner. Each of these phenomena deserves a separate review papers, interested readers are respectfully referred to them. The choice of milestones in the field of low-dimensional magnetism is highly debatable. There cannot be unambiguous criteria for importance, timeliness or impact on the scientific community. Several advanced models and concepts of low-dimensional magnetism, for example the BKT transition or the Kitaev model, are still waiting for a rigorous experimental verification. Quite recently, a new member of honeycomb iridates family, Cu 2 IrO 3 , becomes available. Its C 2/c structure with bond angles close to 120° fits almost perfectly the Kitaev model. Although Cu 2 IrO 3 experiences weak magnetic order at 2.7 K, its high frustration ratio of about 40 and sensitivity of the transition to magnetic field evidences its proximity to quantum spin liquid state. 112 Similarly, a new candidate for the realization of quantum spin liquid state on a kagome lattice has appeared recently. It is kapellasite-type cuprate YCu 3 (OH) 6 Cl 3 where no mixing of Y 3+ and Cu 2+ suggests even better realization of perfect kagome than herbertsmithite. 113 Despite high Curie–Weiss temperature of about 100 K this compound exhibit no long-range order down to 2 K. The list of chosen spin-gap compounds is given in Table 1 . There are not many, and the gapless spin-liquids are even scarcer. Fortunately, every new compound with an exotic ground state and non-trivial excitations brings new colors to the palette of quantum cooperative phenomena in solids and brings new inspiration to researches concentrated on this fascinating topic.

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Acknowledgements

The useful comments of Peter Lemmens, Hiroshi Kageyama and John Coulson are gratefully acknowledged. Support of Russian Foundation for Basic Research through grants 17-02-00211, 17-52-45014 and 18-02-00326 is acknowledged. This work has been supported also by the Russian Ministry of Education and Science of the Russian Federation through NUST «MISiS» grant К2-2017-084 and by the Act 211 of the Government of Russia, contracts 02.A03.21.0004 and 02.A03.21.0011.

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Alexander Vasiliev, Olga Volkova, Elena Zvereva & Maria Markina

National Research South Ural State University, Chelyabinsk, 454080, Russia

Alexander Vasiliev, Olga Volkova & Elena Zvereva

National University of Science and Technology “MISiS”, Moscow, 119049, Russia

Alexander Vasiliev & Olga Volkova

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A.V. conceived the outline of the paper and wrote “Chains, phase transitions, long-range order” and “Ladders, Nersesyan–Tsvelik network”. O.V. wrote “Chains, spin liquids” and “Chains, phase transitions, spin gap” sections. E.Z. wrote “Layers, triangular, kagome and honeycomb lattices” section. M.M. wrote “Dimers, Shastry–Sutherland network” and “Dimers, Bose–Einstein condensation” sections. All authors contributed to “Introduction” and “Conclusion” sections.

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Vasiliev, A., Volkova, O., Zvereva, E. et al. Milestones of low-D quantum magnetism. npj Quant Mater 3 , 18 (2018). https://doi.org/10.1038/s41535-018-0090-7

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Received : 29 September 2017

Revised : 14 February 2018

Accepted : 26 February 2018

Published : 28 March 2018

DOI : https://doi.org/10.1038/s41535-018-0090-7

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