Mobility Edge and Level Statistics of Random Tight-Binding Hamiltonians

TL;DR

This paper introduces a high-resolution, finite size scaling method to accurately locate the mobility edge and critical exponent in disordered tight-binding models, avoiding mixing of energy levels.

Contribution

It presents a novel approach that precisely estimates the mobility edge and critical exponent without broad energy averaging, applicable to complex physical models.

Findings

Accurate estimation of the mobility edge in cubic lattices.

Precise determination of the critical exponent.

Method avoids mixing of extended and localized levels.

Abstract

The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus approaching the critical point very closely and with high energy resolution. By finite size scaling the method is shown to provide a very accurate estimate of the mobility edge and of the critical exponent for a cubic lattice with lorentzian distributed diagonal disorder. Since no averaging in wide energy windows is required, the method appears as a powerful tool for locating the mobility edges in more complex models of real physical systems.