Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

Abstract

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 ${\Delta }_q=2q(1-q)[b_0+b_1(q-1/2{)}^2+...]$, with $b_0=0.1291\pm 0.0002$ and $b_1=0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.

4 pages, 4 figures

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