Ground State Degeneracy in the Levin-Wen Model for Topological Phases

Abstract

We study properties of topological phases by calculating the ground state degeneracy (GSD) of the 2d Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always non-degenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.

8 pages, 2 figures. v2: reference added; v3: two appendices added

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Wilson Line Picture of Levin-Wen Partition Functions
• Braid Group, Gauge Invariance and Topological Order
• Tensor-product representations for string-net condensed states

Cited by in corpus (29)

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• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Full Dyon Excitation Spectrum in Generalized Levin-Wen Models
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• Generalized string-net models: A thorough exposition
• Cage-Net Fracton Models
• Partition function of the Levin-Wen model
• Quantum gravity kinematics from extended TQFTs
• Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
• Boundary Hamiltonian theory for gapped topological phases on an open surface
• String-Net Models with $Z_N$ Fusion Algebra
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems
• Boundary Hamiltonian theory for gapped topological orders
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• Topological orders and factorization homology
• Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
• Jones index, secret sharing and total quantum dimension
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• On Quantum Entanglement in Topological Phases on a Torus
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview
• Topological and nontopological degeneracies in generalized string-net models
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• From effective Hamiltonian to anomaly inflow in topological orders with boundaries
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization