Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents Delta(q) characterizing anomalous scaling of wave function moments at the quantum Hall transition. The result reads Delta(q)=2q(1-q)[b(0)+b(1)(q-1/2)(2)+center dot center dot center dot], with b(0)=0.1291 +/- 0.0002 and b(1)=0.0029 +/- 0.0003. The central finding is that the spectrum is not exactly parabolic: b(1)not equal 0. 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.