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arXiv · 1605.07194

Signatures of broken parity and time-reversal symmetry in generalized string-net models

Ethan Lake·Yong-Shi Wu
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Abstract

We study indicators of broken time-reversal and parity symmetries in gapped topological phases of matter. We focus on phases realized by Levin-Wen string-net models, and generalize the string-net model to describe phases which break parity and time-reversal symmetries. We do this by introducing an extra degree of freedom into the string-net graphical calculus, which takes the form of a branch cut located at each vertex of the underlying string-net lattice. We also work with string-net graphs defined on arbitrary (non-trivalent) graphs, which reveals otherwise hidden information about certain configurations of anyons in the string-net graph. Most significantly, we show that objects known as higher Frobenius-Schur indicators can provide several efficient ways to detect whether or not a given topological phase breaks parity or time-reversal symmetry.

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Ethan Lake, Yong-Shi Wu. 2016-09-21. Signatures of broken parity and time-reversal symmetry in generalized string-net models. https://doi.org/10.1103/physrevb.94.115139

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