Non-universality of Anderson localization in short-range correlated disorder

TL;DR

This paper develops an analytic theory showing that short-range correlations in disordered potentials can cause significant anomalies in Anderson localization, challenging the belief in universal scaling behavior.

Contribution

It reveals that even minimal correlations in the potential can lead to strong localization anomalies and violate single parameter scaling, supported by parameter-free numerical simulations.

Findings

Correlations induce anomalies in localization length and density of states

Single parameter scaling can be completely violated due to correlations

Numerical results confirm the theoretical predictions without adjustable parameters

Abstract

We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results of numerical simulations are in full agreement with our theory, with no adjustable parameters.