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Multifractality of wavefunctions at the quantum Hall transition revisited

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

We investigate numerically the statistics of wavefunction amplitudes $ψ({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|ψ|^2$ is log-normal, so that the multifractal spectrum $f(α)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.

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F. Evers, A. Mildenberger, A. D. Mirlin. 2001-05-15. Multifractality of wavefunctions at the quantum Hall transition revisited. https://doi.org/10.1103/physrevb.64.241303

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