Identifying Quantum Topological Phases Through Statistical Correlation

TL;DR

This paper explores using a statistical distance measure called indistinguishability to identify topological order in quantum models, demonstrating its effectiveness on the toric code and fractional quantum Hall systems.

Contribution

It introduces a generic statistical tool for detecting topological phases and highlights differences in symmetry properties between models.

Findings

Indistinguishability successfully identifies topological order in both models.

The measure reveals key symmetry distinctions in different topological phases.

Supports the use of statistical distances as a universal diagnostic for topological order.

Abstract

We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order. We apply this measure to the toric code and two fractional quantum Hall models. We find that topologically ordered states can be identified with the indistinguishability for both models. Calculations with the indistinguishability also underscore a key distinction between symmetries that underlie topological order in the toric code and quantum Hall models.