Conductivity in a disordered one-dimensional system of interacting fermions

TL;DR

This study numerically investigates the dynamical conductivity of a disordered one-dimensional interacting fermion system at high temperatures, revealing how conductivity scales with disorder and interaction, and suggesting a link to the effective localization length.

Contribution

It provides new insights into the interplay between disorder and interactions in one-dimensional fermionic systems, especially regarding conductivity behavior and localization.

Findings

d.c. conductivity scales linearly with interaction strength

conductivity depends exponentially on disorder

absence of many-body localization linked to increased localization length

Abstract

Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing d.c. transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the d.c. conductivity sigma0 scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase of the effective localization length with the interaction.