Level statistics across the many--body localization transition

TL;DR

This paper investigates the spectral level statistics across the many-body localization transition, proposing a generalized short-range plasma model that accurately captures critical and disorder-induced spectral features in various quantum systems.

Contribution

It introduces a novel weighted short-range plasma model that effectively describes level statistics during the many-body localization transition, including critical and disorder effects.

Findings

The model accurately fits level spacing distributions and number variance.

It captures critical level statistics at maximum inter-sample fluctuations.

The model applies to spin, Bose-Hubbard, and Fermi-Hubbard systems.

Abstract

Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random and quasi-random disorder, showing the effects due to Griffiths rare events for the former case. It is argued that the transition in the case of random disorder exhibits universal features that are identified by constructing an appropriate model of intermediate spectral statistics which is a generalization of the family of short-range plasma models. The considered weighted short-range plasma model yields a very good agreement both for level spacing distribution including its exponential tail and the number variance up to tens of level spacings outperforming previously proposed models. In particular, our model grasps the critical level statistics which arise at disorder strength for which the inter-sample fluctuations are the strongest. Going beyond the paradigmatic examples of many-body localization in spin systems, we show that the considered model also grasps the level statistics of disordered Bose- and Fermi-Hubbard models. The remaining deviations for long-range spectral correlations are discussed and attributed mainly to the intricacies of level unfolding.