Abstract
We numerically investigate the single parameter scaling (SPS) hypothesis in a non-interacting one-dimensional correlated Anderson model. In particular, we examine the role of spatial correlation in disorder potentials on the SPS hypothesis at the band center. We report numerical calculations of the cumulants ratio of the distribution of the logarithmic conductance based on the linearized Landauer formalism at zero temperature. Our numerical finding indicates the validity of the SPS hypothesis at critical correlation exponent αc in the thermodynamic limit. However, we observe the break down of the SPS theory for α≠αc, where cumulants ratio deviates significantly from the previous theoretical SPS estimate in the correlated Anderson model.
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