Multifractality at the spin quantum Hall transition

Abstract

Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\ensuremath{\eta}$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the ${r}^{\ensuremath{-}1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close to parabolic, ${\ensuremath{\Delta}}_{q}\ensuremath{\simeq}q(1\ensuremath{-}q)/8$ and ${X}_{q}\ensuremath{\simeq}q(3\ensuremath{-}q)/4.$