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The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $Delta_q$ governing the scaling of moments $<|psi|^{2q}>sim L^{-qd-Delta_q}$ with the system size $L$ and the spatial decay of wave function correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values $Delta_2=-1/4$ and $Delta_3=-3/4$. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation $Delta_qsimeq q(1-q)/8$ but shows detectable deviations. We also study statistics of the two-point conductance $g$, in particular, the spectrum of exponents $X_q$ characterizing the scaling of the moments $<g^q >$. Relations between the spectra of critical exponents of wave functions ($Delta_q$), conductances ($X_q$), and Green functions at the localization transition with a critical density of states are discussed.
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 functi
We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $Delta_q$ characterizing anomalous scaling of wave function moments $<|psi|^{2q}>$ at the quantum Hall transition. The result reads $Delta_q = 2q(1-q)[b_0 +
Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconducto
We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition w
We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare d