Nonperturbative Renormalization Group Function for Quantum Hall Plateau Transitions Imposed by Global Symmetries

TL;DR

This paper develops a nonperturbative renormalization group theory for quantum Hall transitions, imposing global symmetries to analytically determine critical exponents that match experimental and numerical results.

Contribution

It introduces a unified, nonperturbative RG framework for quantum Hall transitions based on global symmetries, providing analytical expressions for critical exponents.

Findings

Critical exponent ν ≈ 2.1 matches experiments

Irrelevant scaling index y ≈ 0.3 agrees with numerics

Analytical RG flow form derived from symmetry constraints

Abstract

As a unified theory of integer and fractional quantum Hall plateau transitions, a nonperturbative theory of the two-parameter scaling renormalization group function is presented. By imposing global symmetries known as ``the law of corresponding states'', we seek a possible form of renormalization group flows. Asking for consistency with the result from weak-localization perturbation theory, such restriction is so intense that we can analytically determine its concrete form. Accordingly, the critical exponent $\nu$ and the irrelevant scaling index $y$ are obtained analytically and turn out to be irrational. Their values ($\nu\approx 2.1$, $y\approx 0.3$) agree favorably well with experiments and numerics.