Accuracy of the coherent potential approximation for a one-dimensional array with a Gaussian distribution of fluctuations in the on-site potential

TL;DR

This paper assesses the accuracy of the coherent potential approximation (CPA) in modeling a one-dimensional array with Gaussian-distributed on-site potential fluctuations, finding it to be highly accurate and potentially exact.

Contribution

It demonstrates that CPA closely matches numerical mode-counting results for this model, suggesting CPA's potential exactness in this context.

Findings

CPA agrees well with mode-counting results

CPA may be exact for the one-dimensional Gaussian disorder model

Inverse localization length can be approximated by the decay length of a localized state

Abstract

We investigate the accuracy of the coherent potential approximation (CPA) for a one-dimensional array with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the on-site potential. The CPA values of the integrated density of states and the inverse localization length are compared with the results of mode-counting studies carried out on arrays of 107 - 108 sites. Good agreement is obtained suggesting that the CPA may be exact for this model. We also consider the asymptotic behavior of the inverse localization length and show that it can be approximated by the reciprocal of the decay length of a state localized about a single, strongly perturbed site in an otherwise perfect lattice.