Citation: Lake, Ethan, and Yong-Shi Wu. "Signatures of broken parity and time-reversal symmetry in generalized string-net models." Physical Review B 94.11 (2016): 115139.
Web: https://arxiv.org/abs/1605.07194
Tags: Modular-tensor-categories, Kitaev-quantum-double
This paper highlights an important but subtle point about generalized string-net models. Namely, when you generalize the Levin-Wen model beyond phases with tetrahedral symmetry, then there will not necessarily be time-reversal symmetric (or, equivalently, non-chiral). The most pertinent example given in this paper is the Tambara-Yamagami fusion category TY(Z_3). This is a perfectly good unitary fusion category, but its quantum double is not time-reversal symmetric!
An interesting observation is that this paper does not cite
> Lin, Chien-Hung, Michael Levin, and Fiona J. Burnell. "Generalized string-net models: A thorough exposition." Physical Review B 103.19 (2021): 195155.
It seems that these were written largely independently of one another. However, they contain largely the same information. They even both use the TY(Z_3) example! The conventions of Lin-Levin-Burnell have been more favored by the community, and so this paper has been relatively unappreciated in comparison.