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

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

1998-10-22

arxiv.org/abs/cond-mat/9810286v1

Ann. Phys. (Leipzig) 7 (1998), 442-451

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, LaTeX2e, 7 fig, invited talk at PILS (Percolation, Interaction, Localization: Simulations of Transport in Disordered

Scientific paper

10.1002/(SICI)1521-3889(199811)7

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 \nu = 1.1 \pm 0.2 and the critical spectral compressibility k_c \approx 0.5.

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