Universal spectral form factor for many-body localization

TL;DR

This paper derives an exact analytical expression for the spectral form factor in many-body localized systems, demonstrating a universal regime that aligns with numerical results across different models.

Contribution

It provides the first exact analytical form of the spectral form factor for Poisson spectra in many-body localization, revealing universal features.

Findings

Analytical spectral form factor matches numerical results

Universal regime insensitive to density of states

Applicable to different MBL models

Abstract

We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body-localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.