Transport in a disordered tight-binding chain with dephasing

TL;DR

This paper analyzes how dephasing and disorder affect transport in a disordered tight-binding chain, revealing optimal dephasing for maximum conductivity and resonance phenomena in periodic disorder cases.

Contribution

It provides an analytical study of conductivity dependence on dephasing and disorder in a disordered XX spin chain, including novel resonance effects and scaling behaviors.

Findings

Conductivity peaks at an optimal dephasing strength.

Resonance with two maxima in periodic disorder.

Disorder on a fraction of sites yields similar conductivity with rescaled disorder.

Abstract

We study transport properties of a disordered tight-binding model (XX spin chain) in the presence of dephasing. Focusing on diffusive behavior in the thermodynamic limit at high energies, we analytically derive the dependence of conductivity on dephasing and disorder strengths. As a function of dephasing, conductivity exhibits a single maximum at the optimal dephasing strength. The scaling of the position of this maximum with disorder strength is different for small and large disorder. In addition, we study periodic disorder for which we find a resonance phenomenon, with conductivity having two maxima as a function of dephasing strength. If disorder is nonzero only at a random fraction of all sites, conductivity is approximately the same as in the case of a disorder on all sites but with a rescaled disorder strength.