Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups

Abstract

We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev-Viro TQFT is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models.

39 pages, tikz figures

References in corpus (5)

• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Mapping Class Group Representations From Non-Semisimple TQFTs
• Modified graded Hennings invariants from unrolled quantum groups and modified integral
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules

Cited by in corpus (2)

• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• A non-semisimple non-invertible symmetry