Multifractality of wavefunctions at the quantum Hall transition revisited

Abstract

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

4 pages Latex

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