Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition

Understand

We study a one-dimensional (1d) XXZ spin-chain in a random field on the metallic side of the many-body localization transition by level statistics.

• For a fixed interaction, and intermediate disorder below the many-body localization transition, we find that, asymptotically, the number variance grows faster than linear with a disorder dependent exponent.
• This is consistent with the existence of an anomlaous Thouless energy in the spectrum.
• In non-interacting disordered metals this is an energy scale related to the typical time for a particle to diffuse across the sample.