Generalized string-nets for unitary fusion categories without tetrahedral symmetry

Abstract

The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. However, the original construction is not applicable to all unitary fusion category since some additional symmetries for the $F$-symbols are imposed. In particular, the so-called tetrahedral symmetry is not fulfilled by many interesting unitary fusion categories. In this paper, we present a generalized construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories that works without requiring these additional symmetries. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.

24 pages, 5 figures

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• Mapping between Morita equivalent string-net states with a constant depth quantum circuit
• Universal lower bound on topological entanglement entropy
• Multipartite edge modes and tensor networks
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Galois conjugates of String-net Model
• Topological and nontopological degeneracies in generalized string-net models
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• Finite-temperature properties of string-net models
• Rényi-like entanglement probe of the chiral central charge
• Extended string-net models with all anyons at finite temperature
• Categorical Quantum Volume Operator