Hidden Scaling in the Quantum Hall Metal-Insulator Transition

TL;DR

This paper reveals a hidden infrared scaling phenomenon in the quantum Hall metal-insulator transition, demonstrating how extended self-similarity can improve multifractal exponent estimation despite finite size effects.

Contribution

It uncovers a hidden scaling behavior in the transition and introduces an extended self-similarity analysis to better evaluate multifractal exponents in small systems.

Findings

Existence of extended self-similarity in the transition

Improved multifractal exponent estimation for negative orders

Finite size effects impact the accuracy of multifractal spectra

Abstract

Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal scaling, we clearly verify the existence of extended self-similarity -- a hidden infrared scaling phenomenon related to the peculiar form of the crossover at the onset of nonmultifractal behavior. As finite size effects get stronger for structure functions with negative orders, the parabolic approximation for the multifractal spectrum loses accuracy. However, by means of an extended self-similarity analysis, an improved evaluation of the multifractal exponents is attained for negative orders too, rendering them consistent with previous results, which rely on computations performed for considerably larger systems.