Multifractality at the quantum Hall transition: beyond the parabolic paradigm.
We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents Deltaq characterizing anomalous scaling of wave function moments |psi|2q at the quantum Hall transition. The result reads Deltaq=2q(1-q)[b0+b1(q-1/2)2+cdots, three dots, centered], with b0=0.1291+/-0.0002 and b1=0.0029+/-0.0003. The central finding is that the spectrum is not exactly parabolic: b1 not equal0. This rules out a class of theories of the Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.
Institut für Nanotechnologie, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany.
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Evers
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Mildenberger
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Mirlin