Zusammenfassung
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 Δq governing the scaling of moments lang|ψ|2q}rang ~ L−qd−Δq with the system size L and the spatial decay of wavefunction correlations. Two- and three-point correlation functions are calculated ...
Zusammenfassung
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 Δq governing the scaling of moments lang|ψ|2q}rang ~ L−qd−Δq 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 Δ2 = −1/4 and Δ3 = −3/4. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation Δq sime q(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 langgqrang. Relations between the spectra of critical exponents of wavefunctions (Δq), conductances (Xq) and Green functions at the localization transition with a critical density of states are discussed.
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