Multifractality at the Quantum Hall Transition: Beyond the Parabolic Paradigm
Multifractality at the Quantum Hall Transition: Beyond the Parabolic Paradigm
We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents ${\ensuremath{\Delta}}_{q}$ characterizing anomalous scaling of wave function moments $⟨|\ensuremath{\psi}{|}^{2q}⟩$ at the quantum Hall transition. The result reads ${\ensuremath{\Delta}}_{q}=2q(1\ensuremath{-}q)[{b}_{0}+{b}_{1}(q\ensuremath{-}1/2{)}^{2}+\ensuremath{\cdots}]$, with ${b}_{0}=0.1291\ifmmode\pm\else\textpm\fi{}0.0002$ and ${b}_{1}=0.0029\ifmmode\pm\else\textpm\fi{}0.0003$. The central finding is that the spectrum is not exactly parabolic: ${b}_{1}\ensuremath{\ne}0$. This rules out a …