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Dimensionality dependence of the wave function statistics at the Anderson transition

A. Mildenberger·F. Evers·A. D. Mirlin
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Abstract

The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.

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A. Mildenberger, F. Evers, A. D. Mirlin. 2001-11-06. Dimensionality dependence of the wave function statistics at the Anderson transition. https://doi.org/10.1103/physrevb.66.033109

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