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 $\eta$ 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 $X_q\simeq q(3-q)/4$.

4 pages, 3 figures

References in corpus (5)

• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Multifractality of wavefunctions at the quantum Hall transition revisited
• Quantum and classical localisation, the spin quantum Hall effect and generalisations
• Renormalization group for network models of Quantum Hall transitions
• Mobility edge scaling at semiclassical and dissipative Hall transitions

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