Multifractality of wave functions at the quantum Hall transition revisited

We investigate numerically the statistics of wave function amplitudes $\psi \left(\mathbf{r}\right)$ 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 $f\left(\alpha \right)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.