Universal dynamics of density correlations at the transition to many-body localized state

TL;DR

This study numerically investigates dynamical density correlations in disordered one-dimensional fermionic systems, revealing universal behavior and a transition to many-body localization characterized by abrupt changes and logarithmic time dependence.

Contribution

It demonstrates that the transition to many-body localization exhibits universal dynamical exponents and features a logarithmic variation of correlations over a wide time window.

Findings

Density-wave correlations change abruptly with disorder.

Long-time correlations are nonvanishing in the nonergodic phase.

Correlations show logarithmic variation in time near the transition.

Abstract

Within one-dimensional disordered models of interacting fermions we perform a numerical study of several dynamical density correlations, which can serve as hallmarks of the transition to the many-body localized state. Results confirm that density-wave correlations exhibit quite abrupt change with the increasing disorder, with nonvanishing long-time value characteristic for nonergodic phase. In addition, our results reveal in a wide time-window a logarithmic variation of correlations in time, which we can bring in connection with the anomalous behavior of the dynamical conductivity near the transition. Our result support the view that transition to many-body localization can be characterized by universal dynamical exponents.