Critical level statistics at the Anderson transition in four-dimensional disordered systems

Abstract

The level spacing distribution is numerically calculated at the disorder-induced metal–insulator transition for dimensionality d = 4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d = 3 and to become closer to the Poisson limit of uncorrelated spectra. Using the finite size scaling analysis for the probability distribution Qn(E) of having n levels in a given energy interval E we find the critical disorder Wc = 34.5 ± 0.5, the correlation length exponent ν = 1.1 ± 0.2 and the critical spectral compressibility κc ≈︂ 0.5.