Symmetry Enriched Phases via Pseudo Anyon Condensation

Abstract

We show that a large class of symmetry enriched (topological) phases of matter in 2+1 dimensions can be embedded in "larger" topological phases- phases describable by larger hidden Hopf symmetries. Such an embedding is analogous to anyon condensation, although no physical condensation actually occurs. This generalizes the Landau-Ginzburg paradigm of symmetry breaking from continuous groups to quantum groups- in fact algebras- and offers a potential classification of the symmetry enriched (topological) phases thus obtained, including symmetry protected trivial phases as well, in a unified framework.

5 pages and 2 pages supplementary material

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• Ground State Degeneracy of Topological Phases on Open Surfaces
• Generalized ADE Classification of Gapped Domain Walls
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Spectroscopic signatures of crystal momentum fractionalization
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
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• A systematic construction of gapped non-liquid states
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• Lattice model constructions for gapless domain walls between topological phases
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• Symmetry reduction induced by anyon condensation: a tensor network approach
• Non-Liquid Cellular States
• Families of Gapped Interfaces Between Fractional Quantum Hall States
• No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids
• Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
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• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries