Universal spectral form factor for many-body localization

Abstract

We theoretically study universal correlations present in the spectrum of many-body-localized systems. We obtain an exact analytical expression for the spectral form factor of Poisson spectra and show that it agrees well with numerical results on two models exhibiting a many-body-localization: a disordered quantum spin chain and a phenomenological l-bit model based on the existence of local integrals of motion. We find that the functional form of the Poisson spectral form factor is distinct from but complementary to the universal expectation of quantum chaotic systems obtained from random matrix theory.