Determining topological order from a local ground state correlation function

TL;DR

This paper presents a local method to determine the topological indices of insulators and quantum Hall systems from ground-state correlations, applicable even with disorder and weak interactions.

Contribution

It introduces an algorithm to extract topological indices locally from ground-state correlation functions, extending topological characterization to disordered and interacting systems.

Findings

The Z index can be determined locally from ground-state correlations.

The method is robust against disorder.

It generalizes to include weak interactions.

Abstract

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological insulators and the Z index of the integer quantum Hall effect manifest themselves locally. We do so by providing an algorithm for determining these indices from a local equal time ground-state correlation function at any convenient boundary conditions. Our procedure is unaffected by the presence of disorder and can be naturally generalized to include weak interactions. The locality of these topological indices implies bulk-edge correspondence theorem.