Energy level statistics at the metal-insulator transition in the Anderson model of localization with anisotropic hopping

TL;DR

This paper uses energy level statistics to analyze the metal-insulator transition in an anisotropic Anderson model, confirming critical disorder values and characterizing spectral behavior across phases.

Contribution

It introduces energy level statistics as a new method to characterize the MIT in anisotropic Anderson models, complementing previous transfer-matrix and multifractal analyses.

Findings

Level spacing distribution transitions from GOE to Poisson with increasing disorder

Spectral rigidity analysis confirms critical disorder values from other methods

Energy level statistics effectively characterize the MIT in anisotropic systems

Abstract

Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders $W_c$ have been obtained within the accuracy of the data. We now employ energy level statistics (ELS) to further characterize the MIT. We find a crossover of the nearest-neighbor level spacing distribution $P(s)$ from GOE statistics at small disorder indicating metallic behavior to the Poisson distribution at large disorder characteristic for localized states. An analysis of the system size dependence of the spectral rigidity $\Delta_3(L)$ confirms the values of $W_c$ from TMM and MFA.