Charged Topological Entanglement Entropy

TL;DR

This paper introduces a charged entanglement entropy as a novel measure to detect symmetry protected topological (SPT) phases in 2+1 dimensions, which are otherwise undetectable by traditional topological entanglement entropy.

Contribution

It demonstrates that the universal part of the charged entanglement entropy can identify non-trivial SPT phases, linking it to quasiparticle braiding statistics.

Findings

Charged entanglement entropy is non-zero for non-trivial SPT phases.

It provides a new method to classify SPT phases.

The measure relates to quasiparticle braiding statistics.

Abstract

A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry protected topological (SPT) phases in 2+1 dimensional space-time by using this charged entanglement entropy. SPT phases are short range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. We demonstrate that the universal part of the charged entanglement entropy is non-zero for non-trivial SPT phases and therefore it is a useful measure to detect short range entangled topological phases. We also discuss that the classification of SPT phases based on the charged topological entanglement entropy is related to that of the braiding statistics of quasiparticles.