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Multifractality at the Quantum Hall Transition: Beyond the Parabolic Paradigm

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Evers, Ferdinand ; Mildenberger, A. ; Mirlin, A. D.
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Date of publication of this fulltext: 02 Jul 2021 11:13


We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents Δq characterizing anomalous scaling of wave function moments ⟨|ψ|2q⟩ at the quantum Hall transition. The result reads Δq=2q(1−q)[b0+b1(q−1/2)2+⋯], with b0=0.1291±0.0002 and b1=0.0029±0.0003. The central finding is that the spectrum is not exactly parabolic: b1≠0. This rules out a class of theories of the ...


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