Proposal for many-body quantum chaos detection with single-site measurements

TL;DR

This paper proposes a method to detect many-body quantum chaos using only single-site measurements of a disordered spin chain, making experimental detection more feasible with current technology.

Contribution

It introduces a practical approach to identify quantum chaos through local observables, enabling experimental detection in small systems.

Findings

Single-site observables can indicate level statistics of quantum chaos.

Detection is feasible with current experimental precision and timescales.

Method is applicable to disordered spin-1/2 chains.

Abstract

We demonstrate that the long-time dynamics of an observable associated with a single lattice site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, a widely used diagnostic of quantum chaos. In particular, we focus on the partial survival probability and spin autocorrelation function at a single site, both evolved under a disordered spin-1/2 chain, which is a setup realizable in current experimental platforms. Given the precision and timescales currently achievable, our results indicate that the detection of many-body quantum chaos is feasible, but constrained to small system sizes.