Generalized string-nets for unitary fusion categories without tetrahedral symmetry

• URL: http://arxiv.org/abs/2004.07045v1
• Date: Wed, 15 Apr 2020 12:21:28 GMT
• Title: Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Authors: Alexander Hahn and Ramona Wolf
• Abstract summary: We present a general construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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