We extend the multifractal analysis of the statistics of critical wave functions

Based on differences of generalized Rényi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two-measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau-band is analyzed.

We study the statistics of eigenvectors in correlated random band matrix models. These models are characterized by two parameters, the band width B(N ) of a Hermitian N × N matrix and the correlation parameter C(N ) describing correlations of matrix elements along diagonal lines. The correlated band matrices show a much richer phenomenology than models without correlation as soon as the correlation parameter scales sufficiently fast with matrix size. In particular, for B(N ) ∼ √ N and C(N ) ∼ √ N , the model shows a localization-delocalization transition of the quantum Hall type.

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