Multifractality of wave functions at the quantum Hall transition revisited

Abstract

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.