Localization of interacting fermions at high temperature

TL;DR

This paper investigates the possibility of many-body localization at high temperatures in strongly disordered, weakly interacting fermionic systems, using numerical spectral analysis of small one-dimensional models.

Contribution

It provides a detailed numerical study of spectral statistics in high-temperature regimes, highlighting challenges in definitively identifying many-body localization.

Findings

Spectral statistics transition from Wigner-Dyson to Poisson with increasing disorder.

Finite-size effects cause the apparent mobility edge to drift as system size increases.

No conclusive evidence for many-body localization at nonzero temperature from spectral data.

Abstract

We suggest that if a localized phase at nonzero temperature $T>0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high. We show that in this high-$T$ regime the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero $T$.