Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

TL;DR

This study provides high-precision numerical evidence that the multifractal spectrum at the quantum Hall transition deviates from a parabolic form, challenging recent theoretical models based on conformal field theories.

Contribution

The paper demonstrates that the multifractal spectrum is not exactly parabolic, offering new insights into the critical behavior at the quantum Hall transition.

Findings

Multifractal spectrum deviates from parabolic form.

Numerical values for spectrum coefficients with high precision.

Challenges existing conformal field theory models.

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.