Multifractality at the spin quantum Hall transition

TL;DR

This paper investigates the critical wave functions at the spin quantum Hall transition, revealing their multifractal nature and contrasting correlation decay with diffusion propagator behavior, supported by numerical and analytical methods.

Contribution

It provides the first detailed analysis of multifractality at the spin quantum Hall transition, including analytical mapping to percolation and numerical verification.

Findings

Correlation decay index η = 1/4

Multifractality spectra are close-to-parabolic

Diffusion propagator decays as r^{-1/2}

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 $\eta$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $\Delta_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$.