Single parameter scaling in the non-Hermitian Anderson model

Abstract

We numerically study the single parameter scaling (SPS) hypothesis in a non-interacting one-dimensional non-Hermitian Anderson model. We examine the role of non-Hermiticity in disorder potential on the SPS hypothesis at the band center. We report numerical calculations of the mean and variance of the distribution of the negative logarithmic conductance based on the linearized Landauer formalism in the perturbative regime at zero temperature. Our numerical finding indicates the violation of the SPS hypothesis for the non-Hermitian Anderson model. In particular, it turns out that the numerical SPS value of the Hermitian Anderson model is twice the magnitude of the SPS value of the non-Hermitian Anderson model for overall energies. Moreover, we obtain a relation between the localization length of the Hermitian and non-Hermitian Anderson models.