Fracton Models on General Three-Dimensional Manifolds

Abstract

Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations (dubbed fractons), and a ground state degeneracy that is robust to local perturbations. However, because previous fracton models have only been defined and analyzed on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.

12 pages, 11 figures

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Cited by in corpus (152)

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• Foliated Quantum Field Theory of Fracton Order
• Fractal Symmetric Phases of Matter
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• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• The low-energy limit of some exotic lattice theories and UV/IR mixing
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• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Fractonic Superfluids
• Pinch Point Singularities of Tensor Spin Liquids
• Crystalline topological phases as defect networks
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Topological Defect Networks for Fractons of all Types
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions
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• Universal entanglement signatures of foliated fracton phases
• Parallelized quantum error correction with fracton topological codes
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• Subsystem Non-Invertible Symmetry Operators and Defects
• Higher order topological superconductors as generators of quantum codes
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
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• Braiding and Gapped Boundaries in Fracton Topological Phases
• Non-Abelian Hybrid Fracton Orders
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Towards a mathematical formalism for classifying phases of matter
• Anisotropic layer construction of anisotropic fracton models
• A systematic construction of gapped non-liquid states
• Sequential Quantum Circuits as Maps between Gapped Phases
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Gauging permutation symmetries as a route to non-Abelian fractons
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• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Fractonic superfluids. (II). Condensing subdimensional particles
• Comments on Foliated Gauge Theories and Dualities in 3+1d
• Compactifying fracton stabilizer models
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Fracton physics of spatially extended excitations
• Fractons from polarons
• Subsystem symmetry enriched topological order in three dimensions
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• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
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• Searching for Fracton Orders via Symmetry Defect Condensation
• Classifying local fractal subsystem symmetry protected topological phases
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• Maxwell theory of fractons
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Fractonic order in infinite-component Chern-Simons gauge theories
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
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• Lieb-Schultz-Mattis type constraints on Fractonic Matter
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• Boundary theory of the X-cube model in the continuum
• Foliated-Exotic Duality in Fractonic BF Theories
• Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Covariant fracton gauge theory with boundary
• Gapped Lineon and Fracton Models on Graphs
• A degeneracy bound for homogeneous topological order
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Tailoring three-dimensional topological codes for biased noise
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
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• Symmetric higher rank topological phases on generic graphs
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
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• Realization of fractonic quantum phases in the breathing pyrochlore lattice
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• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
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• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
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• Designer non-Abelian fractons from topological layers
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• Fracton-like phases from subsystem symmetries
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• Boundary Modes in the Chamon Model
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
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• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Non-Fermi liquid induced by Bose metal with protected subsystem symmetries
• Screw dislocations in the X-cube fracton model
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
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• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
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