Wavefunction statistics and multifractality at the spin quantum Hall transition
Authors: Mirlin A.D.1; Evers F.1; Mildenberger A.1
Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3255-3279(25)
Publisher: Institute of Physics Publishing
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Abstract:
The statistical properties of wavefunctions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put on the determination of the spectrum of multifractal exponents q governing the scaling of moments ||2q} ~ L-qd-q with the system size L and the spatial decay of wavefunction correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values 2 -1/4 and 3 -3/4. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation qq(1 - q)/8, but shows detectable deviations. We also study statistics of the two-point conductance g, in particular, the spectrum of exponents Xq characterizing the scaling of the moments gq. Relations between the spectra of critical exponents of wavefunctions (q), conductances (Xq) and Green functions at the localization transition with a critical density of states are discussed.
Language: English
Document Type: Miscellaneous
Affiliations: 1: Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany
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