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

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.

21 pages (13 + appendices)

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Cited by in corpus (9)

• Generalized string-net models: A thorough exposition
• Towards a mathematical formalism for classifying phases of matter
• Mapping between Morita equivalent string-net states with a constant depth quantum circuit
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• Numerical simulation of non-abelian anyons
• Bound states in string nets
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview
• Anomalies and symmetry fractionalization in reflection-symmetric topological order
• Extended string-net models with all anyons at finite temperature