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At the Anderson transition for power-law random banded matrix ensembles, the distribution functions of the inverse participation ratios are scale-invariant at the critical point and exhibit a power-law asymptotic tail. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

September 15, 2000Physical review. B, Condensed matter250 citationsOpen Access

Multifractality and critical fluctuations at the Anderson transition

AMA. D. MirlinKarlsruhe Institute of Technology FEFerdinand EversUniversity of Regensburg

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Abstract

Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) Pₐ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum, and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as numerically in the full range of couplings.

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