Phys. Rev. B 62, 7920–7933 (2000)Multifractality and critical fluctuations at the Anderson transitionReceived 20 March 2000; revised 28 June 2000; published in the issue dated 15 September 2000 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) Pq 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. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevB.62.7920
DOI:
10.1103/PhysRevB.62.7920
PACS:
72.15.Rn, 71.30.+h, 05.45.Df
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