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Critical level statistics at the Anderson transition in four‐dimensional disordered systems
Author(s) -
Zharekeshev I.Kh.,
Kramer B.
Publication year - 1998
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199811)7:5/6<442::aid-andp442>3.0.co;2-d
Subject(s) - statistical physics , physics , anderson localization , condensed matter physics , statistics , mathematics
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 ± 0.5, the correlation length exponent ν = 1.1 ± 0.2 and the critical spectral compressibility κ c ≈ 0.5.