SciPost Physics

SciPost Phys. 6, 015 (2019) · published 31 January 2019

• doi: 10.21468/SciPostPhys.6.1.015
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Abstract

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In a previous work, we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

• 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]
• Tantivasadakarn et al., Non-Abelian hybrid fracton orders
  Phys. Rev. B 104, 115117 (2021) [Crossref]
• Wen et al., Volume and topological invariants of quantum many-body systems
  Phys. Rev. Research 2, 033030 (2020) [Crossref]
• Kobayashi, Lattice construction of exotic invertible topological phases
  Phys. Rev. B 105, 035153 (2022) [Crossref]
• Fontana et al., Boundary modes in the Chamon model
  SciPost Phys. 15, 010 (2023) [Crossref]
• Tu et al., Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries
  Phys. Rev. Research 3, 043084 (2021) [Crossref]
• Tam et al., Topological Multipartite Entanglement in a Fermi Liquid
  Phys. Rev. X 12, 031022 (2022) [Crossref]
• Nussinov et al., Theorem on extensive spectral degeneracy for systems with rigid higher symmetries in general dimensions
  Phys. Rev. B 107, 045109 (2023) [Crossref]
• Manoj et al., Arboreal topological and fracton phases
  Phys. Rev. B 107, 165136 (2023) [Crossref]
• Tantivasadakarn et al., Hybrid fracton phases: Parent orders for liquid and nonliquid quantum phases
  Phys. Rev. B 103, 245136 (2021) [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]
• Wang et al., Foliated fracton order in the Majorana checkerboard model
  Phys. Rev. B 100, 085127 (2019) [Crossref]
• Shirley et al., Twisted foliated fracton phases
  Phys. Rev. B 102, 115103 (2020) [Crossref]
• Stephen et al., Nonlocal Finite-Depth Circuits for Constructing Symmetry-Protected Topological States and Quantum Cellular Automata
  PRX Quantum 5, 010304 (2024) [Crossref]
• Han et al., Realization of fractonic quantum phases in the breathing pyrochlore lattice
  Phys. Rev. B 105, 235120 (2022) [Crossref]
• Bulmash et al., Gauging fractons: Immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
  Phys. Rev. B 100, 155146 (2019) [Crossref]
• Prem et al., Cage-Net Fracton Models
  Phys. Rev. X 9, 021010 (2019) [Crossref]
• You et al., Fractonic Chern-Simons and BF theories
  Phys. Rev. Research 2, 023249 (2020) [Crossref]
• Devakul et al., Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
  Phys. Rev. Research 2, 012059 (2020) [Crossref]
• Hsin et al., Gapped interfaces in fracton models and foliated fields
  J. High Energ. Phys. 2023, 89 (2023) [Crossref]
• Yan, Hyperbolic fracton model, subsystem symmetry, and holography
  Phys. Rev. B 99, 155126 (2019) [Crossref]
• You, Higher-order topological phase with subsystem symmetries
  New J. Phys. 26, 093028 (2024) [Crossref]
• Zache et al., Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter
  Quantum 6, 702 702 (2022) [Crossref]
• Gromov et al., Colloquium : Fracton matter
  Rev. Mod. Phys. 96, 011001 (2024) [Crossref]
• Slagle et al., Foliated field theory and string-membrane-net condensation picture of fracton order
  SciPost Phys. 6, 043 (2019) [Crossref]
• Yan, Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model
  Phys. Rev. B 100, 245138 (2019) [Crossref]
• Lim et al., Disentangling (2+1)D topological states of matter with entanglement negativity
  Phys. Rev. B 104, 115155 (2021) [Crossref]
• Dua et al., Bifurcating entanglement-renormalization group flows of fracton stabilizer models
  Phys. Rev. Research 2, 033021 (2020) [Crossref]
• Luo et al., Boundary theory of the X-cube model in the continuum
  Phys. Rev. B 106, 195102 (2022) [Crossref]
• Tantivasadakarn et al., Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward
  PRX Quantum 4, 020339 (2023) [Crossref]
• Wang et al., Renormalization of Ising cage-net model and generalized foliation
  Phys. Rev. B 108, 035148 (2023) [Crossref]
• Dua et al., Compactifying fracton stabilizer models
  Phys. Rev. B 99, 245135 (2019) [Crossref]
• Ji et al., Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions
  Phys. Rev. Research 1, 033054 (2019) [Crossref]
• Wen, Systematic construction of gapped nonliquid states
  Phys. Rev. Research 2, 033300 (2020) [Crossref]
• Guo et al., Quantum Phases of Time Order in Many-Body Ground States
  Front. Phys. 10, 847409 (2022) [Crossref]
• Ma et al., Fractonic order in infinite-component Chern-Simons gauge theories
  Phys. Rev. B 105, 195124 (2022) [Crossref]
• Pretko et al., Fracton phases of matter
  Int. J. Mod. Phys. A 35, 2030003 (2020) [Crossref]
• Slagle, Foliated Quantum Field Theory of Fracton Order
  Phys. Rev. Lett. 126, 101603 (2021) [Crossref]
• Prem et al., Gauging permutation symmetries as a route to non-Abelian fractons
  SciPost Phys. 7, 068 (2019) [Crossref]
• Bulmash et al., Braiding and gapped boundaries in fracton topological phases
  Phys. Rev. B 99, 125132 (2019) [Crossref]
• Williamson et al., Fractonic matter in symmetry-enriched U(1) gauge theory
  Phys. Rev. B 100, 125150 (2019) [Crossref]
• Manoj et al., Screw dislocations in the X-cube fracton model
  SciPost Phys. 10, 094 (2021) [Crossref]
• Delfino et al., Anyon condensation web and multipartite entanglement in two-dimensional modulated gauge theories
  Phys. Rev. B 109, 205146 (2024) [Crossref]
• Shirley et al., Foliated fracton order from gauging subsystem symmetries
  SciPost Phys. 6, 041 (2019) [Crossref]
• Schmitz et al., Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter
  Phys. Rev. B 99, 205109 (2019) [Crossref]
• Devakul, Classifying local fractal subsystem symmetry-protected topological phases
  Phys. Rev. B 99, 235131 (2019) [Crossref]
• Fliss, Entanglement in the quantum Hall fluid of dipoles
  SciPost Phys. 11, 052 (2021) [Crossref]
• Shirley et al., Foliated fracton order in the checkerboard model
  Phys. Rev. B 99, 115123 (2019) [Crossref]
• Pai et al., Fracton fusion and statistics
  Phys. Rev. B 100, 195136 (2019) [Crossref]
• Casasola et al., Fractal subsystem symmetries, 't Hooft anomalies, and UV/IR mixing
  Phys. Rev. B 109, 075164 (2024) [Crossref]
• Hsin et al., Comments on foliated gauge theories and dualities in 3+1d
  SciPost Phys. 11, 032 (2021) [Crossref]
• Fontana et al., Field Theories for type-II fractons
  SciPost Phys. 12, 064 (2022) [Crossref]