SciPost Physics

SciPost Phys. 6, 043 (2019) · published 12 April 2019

• doi: 10.21468/SciPostPhys.6.4.043
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.

• He et al., Lieb-Schultz-Mattis–type constraints on fractonic matter
  Phys. Rev. B 101, 165145 (2020) [Crossref]
• Song et al., Topological Defect Network Representations of Fracton Stabilizer Codes
  PRX Quantum 4, 010304 (2023) [Crossref]
• Pretko et al., Fracton phases of matter
  Int. J. Mod. Phys. A 35, 2030003 (2020) [Crossref]
• Luo et al., Boundary theory of the X-cube model in the continuum
  Phys. Rev. B 106, 195102 (2022) [Crossref]
• Wen, Systematic construction of gapped nonliquid states
  Phys. Rev. Research 2, 033300 (2020) [Crossref]
• Grosvenor et al., Space-Dependent Symmetries and Fractons
  Front. Phys. 9, 792621 (2022) [Crossref]
• Dua et al., Bifurcating entanglement-renormalization group flows of fracton stabilizer models
  Phys. Rev. Research 2, 033021 (2020) [Crossref]
• Gorantla et al., Fractons on graphs and complexity
  Phys. Rev. B 106, 195139 (2022) [Crossref]
• Hsin et al., Gapped interfaces in fracton models and foliated fields
  J. High Energ. Phys. 2023, 89 (2023) [Crossref]
• Ohmori et al., Foliated-exotic duality in fractonic BF theories
  SciPost Phys. 14, 164 (2023) [Crossref]
• Hirono et al., A symmetry principle for gauge theories with fractons
  SciPost Phys. 16, 050 (2024) [Crossref]
• Pai et al., Fracton fusion and statistics
  Phys. Rev. B 100, 195136 (2019) [Crossref]
• Gorantla et al., fcc lattice, checkerboards, fractons, and quantum field theory
  Phys. Rev. B 103, 205116 (2021) [Crossref]
• Li et al., Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
  Phys. Rev. B 104, 235127 (2021) [Crossref]
• Gorantla et al., A modified Villain formulation of fractons and other exotic theories
  62, 102301 (2021) [Crossref]
• Poon et al., Quantum phase transition of fracton topological orders
  Phys. Rev. Research 3, 043114 (2021) [Crossref]
• Schmitz et al., Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter
  Phys. Rev. B 99, 205109 (2019) [Crossref]
• Ibieta-Jimenez et al., Fractonlike phases from subsystem symmetries
  Phys. Rev. B 102, 045104 (2020) [Crossref]
• Williamson et al., Designer non-Abelian fractons from topological layers
  Phys. Rev. B 107, 035103 (2023) [Crossref]
• Yan, Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model
  Phys. Rev. B 100, 245138 (2019) [Crossref]
• Sullivan et al., Fractonic topological phases from coupled wires
  Phys. Rev. Research 3, 023123 (2021) [Crossref]
• Fontana et al., Boundary modes in the Chamon model
  SciPost Phys. 15, 010 (2023) [Crossref]
• Chen et al., Fractonic superfluids. II. Condensing subdimensional particles
  Phys. Rev. Research 3, 013226 (2021) [Crossref]
• Prem et al., Gauging permutation symmetries as a route to non-Abelian fractons
  SciPost Phys. 7, 068 (2019) [Crossref]
• Zhou et al., Evolution of dynamical signature in the X-cube fracton topological order
  Phys. Rev. Research 4, 033111 (2022) [Crossref]
• Patra et al., Unveiling topological order through multipartite entanglement
  Phys. Rev. A 105, 052428 (2022) [Crossref]
• Ji et al., Boundary states of three dimensional topological order and the deconfined quantum critical point
  SciPost Phys. 15, 231 (2023) [Crossref]
• Sullivan et al., Planar p-string condensation: Chiral fracton phases from fractional quantum Hall layers and beyond
  Phys. Rev. B 103, 205301 (2021) [Crossref]
• Dua et al., Compactifying fracton stabilizer models
  Phys. Rev. B 99, 245135 (2019) [Crossref]
• Wang et al., Foliated fracton order in the Majorana checkerboard model
  Phys. Rev. B 100, 085127 (2019) [Crossref]
• Brown et al., Parallelized quantum error correction with fracton topological codes
  Phys. Rev. Research 2, 013303 (2020) [Crossref]
• Aasen et al., Topological defect networks for fractons of all types
  Phys. Rev. Research 2, 043165 (2020) [Crossref]
• Fontana et al., Lattice Clifford fractons and their Chern-Simons-like theory
  SciPost Phys. Core 4, 012 (2021) [Crossref]
• Ning et al., Fractionalizing global symmetry on looplike topological excitations
  Phys. Rev. B 105, 205137 (2022) [Crossref]
• Qi et al., Fracton phases via exotic higher-form symmetry-breaking
  Annals of Physics 424, 168360 168360 (2021) [Crossref]
• Zarei et al., Foliated order parameter in a fracton phase transition
  Phys. Rev. B 106, 035101 (2022) [Crossref]
• Shen et al., Fracton topological order at finite temperature
  Phys. Rev. Research 4, L032008 (2022) [Crossref]
• Li et al., Fracton physics of spatially extended excitations
  Phys. Rev. B 101, 245134 (2020) [Crossref]
• Gromov et al., Fracton hydrodynamics
  Phys. Rev. Research 2, 033124 (2020) [Crossref]
• Doshi et al., Vortices as fractons
  Commun Phys 4, 44 (2021) [Crossref]
• Devakul et al., Fractalizing quantum codes
  Quantum 5, 438 438 (2021) [Crossref]
• Osborne et al., Infinite families of fracton fluids with momentum conservation
  Phys. Rev. B 105, 024311 (2022) [Crossref]
• Fuji et al., Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
  Phys. Rev. Research 5, 043108 (2023) [Crossref]
• Fuji, Anisotropic layer construction of anisotropic fracton models
  Phys. Rev. B 100, 235115 (2019) [Crossref]
• Shirley et al., Twisted foliated fracton phases
  Phys. Rev. B 102, 115103 (2020) [Crossref]
• Pérez et al., Asymptotic symmetries and soft charges of fractons
  Phys. Rev. D 106, 044017 (2022) [Crossref]
• Han et al., Realization of fractonic quantum phases in the breathing pyrochlore lattice
  Phys. Rev. B 105, 235120 (2022) [Crossref]
• Hsin et al., Comments on foliated gauge theories and dualities in 3+1d
  SciPost Phys. 11, 032 (2021) [Crossref]
• Stephen et al., Subsystem symmetry enriched topological order in three dimensions
  Phys. Rev. Research 2, 033331 (2020) [Crossref]
• Lake et al., Subdimensional criticality: Condensation of lineons and planons in the X-cube model
  Phys. Rev. B 104, 165121 (2021) [Crossref]
• Gorantla et al., Gapped lineon and fracton models on graphs
  Phys. Rev. B 107, 125121 (2023) [Crossref]
• Gromov, Towards Classification of Fracton Phases: The Multipole Algebra
  Phys. Rev. X 9, 031035 (2019) [Crossref]
• Ebisu et al., Foliated field theories and multipole symmetries
  Phys. Rev. B 109, 165112 (2024) [Crossref]
• Honda et al., Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions
  J. High Energ. Phys. 2023, 188 (2023) [Crossref]
• Bulmash et al., Gauging fractons: Immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
  Phys. Rev. B 100, 155146 (2019) [Crossref]
• You et al., Fractonic Chern-Simons and BF theories
  Phys. Rev. Research 2, 023249 (2020) [Crossref]
• Spieler, Exotic field theories for (hybrid) fracton phases from imposing constraints in foliated field theory
  J. High Energ. Phys. 2023, 178 (2023) [Crossref]
• Tantivasadakarn et al., Hybrid fracton phases: Parent orders for liquid and nonliquid quantum phases
  Phys. Rev. B 103, 245136 (2021) [Crossref]
• Rayhaun et al., Higher-form subsystem symmetry breaking: Subdimensional criticality and fracton phase transitions
  SciPost Phys. 15, 017 (2023) [Crossref]
• Manoj et al., Screw dislocations in the X-cube fracton model
  SciPost Phys. 10, 094 (2021) [Crossref]
• Rudelius et al., Fractons with twisted boundary conditions and their symmetries
  Phys. Rev. B 103, 195113 (2021) [Crossref]
• Pace et al., Position-dependent excitations and UV/IR mixing in the ZN rank-2 toric code and its low-energy effective field theory
  Phys. Rev. B 106, 045145 (2022) [Crossref]
• Li et al., Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
  Phys. Rev. Research 3, 043176 (2021) [Crossref]
• Sous et al., Fractons from polarons
  Phys. Rev. B 102, 214437 (2020) [Crossref]
• Slagle, Foliated Quantum Field Theory of Fracton Order
  Phys. Rev. Lett. 126, 101603 (2021) [Crossref]
• Yi et al., Topological order in interacting semimetals
  Phys. Rev. B 107, 115147 (2023) [Crossref]
• Yuan et al., Fractonic superfluids
  Phys. Rev. Research 2, 023267 (2020) [Crossref]
• Burnell et al., Anomaly inflow for subsystem symmetries
  Phys. Rev. B 106, 085113 (2022) [Crossref]
• Dua et al., Sorting topological stabilizer models in three dimensions
  Phys. Rev. B 100, 155137 (2019) [Crossref]
• You et al., Emergent fractons and algebraic quantum liquid from plaquette melting transitions
  Phys. Rev. Research 2, 013162 (2020) [Crossref]
• Bertolini et al., Covariant fracton gauge theory with boundary
  Phys. Rev. D 108, 025009 (2023) [Crossref]