Twisted foliated fracton phases

Abstract

In the study of three-dimensional gapped models, two-dimensional gapped states should be considered as a free resource. This is the basic idea underlying the notion of `foliated fracton order' proposed in Phys. Rev. X 8, 031051 (2018). We have found that many of the known type I fracton models, although they appear very different, have the same foliated fracton order, known as `X-cube' order. In this paper, we identify three-dimensional fracton models with different kinds of foliated fracton order. Whereas the X-cube order corresponds to the gauge theory of a simple paramagnet with subsystem planar symmetry, the novel orders correspond to twisted versions of the gauge theory for which the system prior to gauging has nontrivial order protected by the planar subsystem symmetry. We present constructions of the twisted models and demonstrate that they possess nontrivial order by studying their fractional excitation contents.

arXiv comment18 pages, 13 figures

References in corpus (75)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• String-net condensation: A physical mechanism for topological phases
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Stabilizer Codes and Quantum Error Correction
• Local stabilizer codes in three dimensions without string logical operators
• Braiding statistics approach to symmetry-protected topological phases
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Condensate induced transitions between topologically ordered phases
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Exotic topological order in fractal spin liquids
• Fracton-Elasticity Duality
• Topological order in an exactly solvable 3D spin model
• The Fracton Gauge Principle
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Glassy quantum dynamics in translation invariant fracton models
• Subsystem symmetry protected topological order
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Anyon condensation and its applications
• Fractal symmetries: Ungauging the cubic code
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Localization in fractonic random circuits
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Dynamical scar states in driven fracton systems
• Fracton topological phases from strongly coupled spin chains
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Topological invariants for gauge theories and symmetry-protected topological phases
• Fractional excitations in foliated fracton phases
• Fractal Symmetric Phases of Matter
• X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
• Classification of subsystem symmetry-protected topological phases
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• On the energy landscape of 3D spin Hamiltonians with topological order
• Twisted Fracton Models in Three Dimensions
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Symmetric Fracton Matter: Twisted and Enriched
• Spurious topological entanglement entropy from subsystem symmetries
• Fractons from Partons
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Symmetric Tensor Gauge Theories on Curved Spaces
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• Stable Gapless Bose Liquid Phases without any Symmetry
• Standard Form of Qudit Stabilizer Groups
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Universal entanglement signatures of foliated fracton phases
• Parallelized quantum error correction with fracton topological codes
• Fracton fusion and statistics
• Foliated fracton order in the checkerboard model
• Higher order topological superconductors as generators of quantum codes
• Symmetry enforced fractonicity and $2d$ quantum crystal melting
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Ungauging quantum error-correcting codes
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Gauging permutation symmetries as a route to non-Abelian fractons
• A Generalization of Non-Abelian Anyons in Three Dimensions
• Compactifying fracton stabilizer models
• Foliated fracton order in the Majorana checkerboard model
• Haah codes on general three manifolds
• Non-Abelian defects in Fracton phase of matter
• Generalized Haah Codes and Fracton Models

Cited by in corpus (44)

• Foliated Quantum Field Theory of Fracton Order
• Long-range entanglement from measuring symmetry-protected topological phases
• Topological Defect Networks for Fractons of all Types
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Anomaly Inflow for Subsystem Symmetries
• Pauli stabilizer models of twisted quantum doubles
• Sorting topological stabilizer models in three dimensions
• Anisotropic layer construction of anisotropic fracton models
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Comments on Foliated Gauge Theories and Dualities in 3+1d
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Type-II fractons from coupled spin chains and layers
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Building models of topological quantum criticality from pivot Hamiltonians
• Fractonic order in infinite-component Chern-Simons gauge theories
• Fractons and exotic symmetries from branes
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Fracton Topological Order at Finite Temperature
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Gapped Lineon and Fracton Models on Graphs
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Fracton Self-Statistics
• Lattice Clifford fractons and their Chern-Simons-like theory
• Competing topological orders in three dimensions: X-cube versus toric code
• Fractons on Graphs and Complexity
• Fractonic topological phases from coupled wires
• Designer non-Abelian fractons from topological layers
• Boundary Modes in the Chamon Model
• Electric Circuit Realizations of Fracton Physics
• Screw dislocations in the X-cube fracton model
• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
• Topological order and Fractons from Gauging Exponential Symmetries
• Renormalization of Ising cage-net model and generalized foliation
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Floating topological phases
• Field Theories for type-II fractons
• Systematic construction of stabilizer codes via gauging abelian boundary symmetries
• Planon-modular fracton orders
• Immersions of punctured 4-manifolds: with applications to Quantum Cellular Automata