Renormalization Group Derivation of the Localization Length Exponent in the Integer Quantum Hall Effect

TL;DR

This paper derives the localization length exponent in the integer quantum Hall effect using a renormalization group approach, finding a universal value of 2 across all Landau levels under specific assumptions.

Contribution

It presents a novel RG-based derivation of the localization length exponent, assuming no Landau level mixing and a scaling law for localization length.

Findings

Localization length exponent ν=2 for all Landau levels

RG transformation of Landau orbitals used in derivation

Assumes no Landau level mixing and existence of a scaling law

Abstract

We compute, neglecting possible effects of subleading irrelevant couplings, the localization length exponent in the integer quantum Hall effect, for the case of white noise random potentials. The result obtained is $\nu=2$ for all Landau levels. Our approach consists in a renormalization group transformation of Landau orbitals, which iterates the generating functional of Green's functions for the localization problem. The value of $\nu$ is obtained from the asymptotic form of the renormalization group mapping. The basic assumptions in our derivation are the existence of a scaling law for the localization length and the absence of Landau level mixing.