Long-ranged spectral correlations in eigenstate phases

TL;DR

This paper investigates non-local spectral correlation measures, such as the spectral form factor and spectral gap density, to effectively distinguish between quantum chaotic and many-body localized phases across various spin chain models.

Contribution

It introduces and analyzes spectral correlation signatures that uniquely identify eigenstate phases, providing a comprehensive framework for classifying disordered quantum systems.

Findings

Spectral form factor and gap density serve as sharp phase indicators.

Universal and non-universal spectral signatures are clarified.

Numerical analysis across different models confirms the effectiveness of these measures.

Abstract

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.