Multifractality at the Quantum Hall Transition: Beyond the Parabolic Paradigm

F. Evers, A. Mildenberger, A. D. Mirlin
2008 Physical Review Letters  
We present an ultra-high-precision numerical study of the spectrum of multifractal exponents Δ_q characterizing anomalous scaling of wave function moments <|ψ|^2q> at the quantum Hall transition. The result reads Δ_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...], 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 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.
doi:10.1103/physrevlett.101.116803 pmid:18851310 fatcat:u4ecuxjy6zdsreztrhdcr7umtu