Transport in a disordered tight-binding chain with dephasing

We studied transport properties of a disordered tight-binding model (XX spin chain) in the presence of dephasing. Focusing on diffusive behaviour in the thermodynamic limit at high energies, we analytically derived 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 disorders. In addition, we studied periodic disorder for which we found a resonance phenomenon, with conductivity having two maxima as a function of dephasing strength. If the disorder is non-zero 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