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.

22+16 pages, 14 figures, 1+3 tables, 3 supplementary files

References in corpus (11)

• Local stabilizer codes in three dimensions without string logical operators
• Entanglement renormalization and topological order
• Fracton topological phases from strongly coupled spin chains
• Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
• Exact entanglement renormalization for string-net models
• Quantum mechanical and information theoretic view on classical glass transitions
• Correlation function diagnostics for type-I fracton phases
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Sorting topological stabilizer models in three dimensions
• Compactifying fracton stabilizer models
• Mixed s-sourcery: Building many-body states using bubbles of Nothing

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• Foliated Quantum Field Theory of Fracton Order
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Topological Defect Networks for Fractons of all Types
• Non-Abelian Hybrid Fracton Orders
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Engineering 3D Floquet codes by rewinding
• Boundary theory of the X-cube model in the continuum
• 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
• Composite subsystem symmetries and decoration of sub-dimensional excitations
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Fracton models from product codes
• Planon-modular fracton orders