Bifurcating entanglement-renormalization group flows of fracton stabilizer models

Abstract

We investigate the entanglement-renormalization group flows of translation-invariant topological stabilizer models in three dimensions. Fracton models are observed to bifurcate under entanglement renormalization, generically returning at least one copy of the original model. Based on this behavior we formulate the notion of bifurcated equivalence for fracton phases, generalizing foliated fracton equivalence. The notion of quotient superselection sectors is also generalized accordingly. We calculate bifurcating entanglement-renormalization group flows for a wide range of examples and, based on those results, propose conjectures regarding the classification of translation-invariant topological stabilizer models in three dimensions.

arXiv comment22+16 pages, 14 figures, 1+3 tables, 3 supplementary files

References in corpus (65)

• Fault-tolerant quantum computation by anyons
• Good Quantum Error-Correcting Codes Exist
• String-net condensation: A physical mechanism for topological phases
• Multiple Particle Interference and Quantum Error Correction
• Entanglement renormalization
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Exotic topological order in fractal spin liquids
• Topological order in an exactly solvable 3D spin model
• Fermions, strings, and gauge fields in lattice spin models
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Entanglement renormalization and topological order
• Fractal symmetries: Ungauging the cubic code
• 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
• Quantum computation with Turaev-Viro codes
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Topological Quantum Glassiness
• Fracton topological phases from strongly coupled spin chains
• Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
• Fractional excitations in foliated fracton phases
• Commuting Pauli Hamiltonians as maps between free modules
• Fractal Symmetric Phases of Matter
• Hamiltonian models for topological phases of matter in three spatial dimensions
• Classification of subsystem symmetry-protected topological phases
• Universal topological phase of 2D stabilizer codes
• Exact entanglement renormalization for string-net models
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Quantum mechanical and information theoretic view on classical glass transitions
• Twisted Fracton Models in Three Dimensions
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Fractons from Partons
• Correlation function diagnostics for type-I fracton phases
• A class of highly entangled many-body states that can be efficiently simulated
• Universal quantum computation using fractal symmetry-protected cluster phases
• Structure of 2D Topological Stabilizer Codes
• Renormalization group constructions of topological quantum liquids and beyond
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Universal entanglement signatures of foliated fracton phases
• Parallelized quantum error correction with fracton topological codes
• Foliated fracton order in the checkerboard model
• Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
• Sorting topological stabilizer models in three dimensions
• Algebraic Methods for Quantum Codes on Lattices
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Gauging permutation symmetries as a route to non-Abelian fractons
• Compactifying fracton stabilizer models
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Foliated fracton order in the Majorana checkerboard model
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• Classifying local fractal subsystem symmetry protected topological phases
• A real space decoupling transformation for quantum many-body systems
• Absence of Finite Temperature Phase Transitions in the X-Cube Model and its ${\mathbb{Z}}_p$ Generalization
• ${\mathbb{Z}}_3$ Topological Order in Face Centered Cubic Quantum Plaquette Model

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• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Engineering 3D Floquet codes by rewinding
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• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Tailoring three-dimensional topological codes for biased noise
• A degeneracy bound for homogeneous topological order
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Non-Liquid Cellular States
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Fractalizing quantum codes
• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• No Strings Attached: Boundaries and Defects in the Cubic Code
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Entanglement renormalization of thermofield double states
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• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Fracton models from product codes
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