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Multifractality of wave functions at the quantum Hall transition revisited

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Evers, Ferdinand ; Mildenberger, A. ; Mirlin, A. D.
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Date of publication of this fulltext: 05 Jul 2021 07:33


We investigate numerically the statistics of wave function amplitudes ψ(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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