Measurement protocol for detecting correlated topological insulators in synthetic quantum systems

TL;DR

This paper introduces a practical measurement protocol for detecting correlated topological insulators in quantum simulators, using a disorder parameter that reveals non-analytical behavior as a signature of topological order.

Contribution

It proposes a unified, experimentally feasible protocol based on measuring a disorder parameter to identify correlated topological insulators in synthetic quantum systems.

Findings

Disorder parameter shows non-analytical dependence for correlated TI

Protocol is robust against decoherence

Numerical and analytical validation of the diagnostic

Abstract

Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI) approach experimental realization in quantum simulators, conventional probes, such as transport measurements, are not easily applicable to these synthetic platforms. In this study, we focus on two examples of correlated TI: a bosonic TI protected by $\mathbb{Z}_2\times U(1)$ symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter $\langle\exp(\mathrm{i}\theta \hat{Q}_A)\rangle$ for a large subregion $A$, with $\hat{Q}_A$ the total charge operator within $A$. Our key finding is that this quantity exhibits non-analytical dependence on $\theta$ for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.