Noise-induced subdiffusion in strongly localized quantum systems

TL;DR

This paper investigates how dephasing noise affects strongly localized quantum systems, revealing a long-lasting subdiffusive transport phase before eventual diffusion restoration, supported by analytical and numerical evidence.

Contribution

It introduces the concept of intermediate-time subdiffusion in noise-affected localized systems and demonstrates its persistence in both single-particle and many-body localized phases.

Findings

Noise induces a long-lived subdiffusive regime.

Normal diffusion is restored at long times via variable-range hopping.

Results are supported by analytical calculations and numerical simulations.

Abstract

We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a parametrically large intermediate-time window. We argue for this intermediate-time subdiffusive regime both analytically and using numerical simulations on single-particle localized systems. Furthermore, we show that normal diffusion is restored in the long-time limit, through processes analogous to variable-range hopping. With numerical simulations based on Lanczos exact diagonalization, we demonstrate that our qualitative conclusions are also valid for interacting systems in the many-body localized phase.