Anderson and many-body localization in the presence of spatially correlated classical noise

TL;DR

This paper investigates how spatially correlated classical noise influences Anderson and many-body localization in a disordered fermionic chain, revealing metastability, stretched-exponential decay, and scaling behaviors relevant for experiments.

Contribution

It demonstrates the impact of spatially correlated classical noise on localization phenomena and introduces a scaling law for relaxation times in such noisy disordered systems.

Findings

Localization signatures persist despite noise.

Metastability and stretched-exponential decay observed.

Scaling behavior of relaxation times identified.

Abstract

We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge density wave state, we find prominent signatures of localization also in the presence of the time-dependent noise, even though the system eventually relaxes to the infinite temperature state. In particular, for sufficiently strong static disorder we observe the onset of metastability, which becomes more prominent the stronger the spatial correlations of the noise. In this regime we find that the imbalance decays as a stretched-exponential - a behavior characteristic of glassy systems. We identify a simple scaling behavior of the relevant relaxation times in terms of the static disorder and of the noise correlation length. We discuss how our results could be exploited to extract information about the localization length in experimental setups.