Mobility Edge and Level Statistics of Random Tight-Binding Hamiltonians

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.