On Enriching the Levin-Wen model with Symmetry

Abstract

Symmetry protected and symmetry enriched topological phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Levin-Wen model for spin/boson systems is an important rigorously solvable model for studying $2D$ topological phases. The input data for the Levin-Wen model is a unitary fusion category, but the same model also works for unitary multi-fusion categories. In this paper, we provide the details for this extension of the Levin-Wen model, and show that the extended Levin-Wen model is a natural playground for the theoretical study of symmetry protected and symmetry enriched topological phases of matter.

arXiv comment21 pages, 6 figures

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• Symmetry enriched string-nets: Exactly solvable models for SET phases
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Hamiltonian models for topological phases of matter in three spatial dimensions
• Lecture Notes on Generalized Symmetries and Applications
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• A systematic construction of gapped non-liquid states
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Topological Quantum Computation with Gapped Boundaries
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• State Sum Invariants of Three Manifolds from Spherical Multi-fusion Categories
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
• Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization