Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes

Abstract

We introduce a new quantity, that we term recoverable information, defined for stabilizer Hamiltonians. For such models, the recoverable information provides a measure of the topological information, as well as a physical interpretation, which is complementary to topological entanglement entropy. We discuss three different ways to calculate the recoverable information, and prove their equivalence. To demonstrate its utility, we compute recoverable information for fracton models using all three methods where appropriate. From the recoverable information, we deduce the existence of emergent $Z_2$ Gauss-law type constraints, which in turn imply emergent $Z_2$ conservation laws for point-like quasiparticle excitations of an underlying topologically ordered phase.

Added additional cluster model calculation (SPT example) and a new section discussing the general benefits of recoverable information

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Cited by in corpus (57)

• Fractons
• Fracton Phases of Matter
• Fracton hydrodynamics
• The Fracton Gauge Principle
• Subsystem symmetry protected topological order
• Fracton Models on General Three-Dimensional Manifolds
• Foliated fracton order from gauging subsystem symmetries
• 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
• Fractional excitations in foliated fracton phases
• Fractal Symmetric Phases of Matter
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Twisted Fracton Models in Three Dimensions
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Many-body localization, symmetry, and topology
• Spurious topological entanglement entropy from subsystem symmetries
• Pinch Point Singularities of Tensor Spin Liquids
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Symmetric Tensor Gauge Theories on Curved Spaces
• Topological Defect Networks for Fractons of all Types
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Fractonic line excitations : an inroad from 3d elasticity theory
• Universal entanglement signatures of foliated fracton phases
• Parallelized quantum error correction with fracton topological codes
• Foliated fracton order in the checkerboard model
• Sorting topological stabilizer models in three dimensions
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Anisotropic layer construction of anisotropic fracton models
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Topological Route to New and Unusual Coulomb Spin Liquids
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Infinite families of fracton fluids with momentum conservation
• Gauging permutation symmetries as a route to non-Abelian fractons
• Compactifying fracton stabilizer models
• Fractons from polarons
• Quantum effects on unconventional pinch point singularities
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
• Fractons from frustration in hole-doped antiferromagnets
• Gauge Structures: From Stabilizer Codes to Continuum Models
• Quantum phase transition of fracton topological orders
• Holographic subdiffusion
• Spectroscopic fingerprints of gapless type-II fracton phases
• Topological Entanglement Entropy in \(d\)-dimensions for Abelian Higher Gauge Theories
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Irrational moments and signatures of higher-rank gauge theories in diluted classical spin liquids
• Entanglement entropy of higher rank topological phases
• Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet