Critical level statistics at the Anderson transition in four-dimensional disordered systems
arXiv:cond-mat/9810286 · doi:10.1002/(SICI)1521-3889(199811)7:5/6<442::AID-ANDP442>3.0.CO;2-D
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 Q_n(E) of having n levels in a given energy interval E we find the critical disorder W_c = 34.5 \pm 0.5, the correlation length exponent ν= 1.1 \pm 0.2 and the critical spectral compressibility k_c \approx 0.5.
10 pages, LaTeX2e, 7 fig, invited talk at PILS (Percolation, Interaction, Localization: Simulations of Transport in Disordered Systems) Berlin, Germany 1998, to appear in Annalen der Physik