QSSEP describes the fluctuations of quantum coherences in the Anderson model

TL;DR

This paper investigates the spatial coherence fluctuations in the 3D Anderson model's metallic phase under non-equilibrium conditions, revealing non-local correlations that align with predictions from the QSSEP, indicating a universal structure in diffusive quantum systems.

Contribution

It demonstrates that the non-local correlations in the Anderson model match those derived from QSSEP, suggesting a universal correlation structure in non-interacting diffusive quantum systems.

Findings

Non-local non-Gaussian correlations are present in the Anderson model.

QSSEP accurately predicts these correlations up to third order.

A link between Anderson model correlations and free probability theory is established.

Abstract

Using the transfer matrix method, we numerically investigate the structure of spatial coherences and their fluctuations in the 3d Anderson model in the metallic phase when driven out-of-equilibrium by external leads at zero temperature and in linear response. We find that the stationary state entails non-local non-Gaussian correlations in the longitudinal direction, which are characteristic of diffusive non equilibrium steady states. These correlations are quantitatively matched, at least up to third order, by those analytically derived in the Quantum Symmetric Simple Exclusion Process (QSSEP) which describes diffusive fermions in 1d subject to dynamical disorder. Furthermore, the large deviation scaling and $U(1)$ invariance of these correlations imply a link between the Anderson model and free probability theory. Our findings suggest the existence of a universal structure of correlations in non-interacting diffusive quantum systems that might be captured by QSSEP.