Anderson Localization and Quantum Hall Effect: Numerical Observation of Two Parameter Scaling

TL;DR

This paper numerically investigates a disordered 2D fermion system in a magnetic field, confirming two-parameter scaling predictions for quantum Hall transitions and providing high-precision RG flow analysis.

Contribution

Introduces a new magnetic gauge for improved RG flow analysis, confirming two-parameter scaling and critical exponents in quantum Hall systems.

Findings

RG flow consistent with Pruisken and Khmelnitskii predictions

Critical exponents match transfer matrix results

Level curvature distribution reflects the necessity of a second parameter

Abstract

A two dimensional disordered system of non-interacting fermions in a homogeneous magnetic field is investigated numerically. By introducing a new magnetic gauge, we explore the renormalization group (RG) flow of the longitudinal and Hall conductances with higher precision than previously studied, and find that the flow is consistent with the predictions of Pruisken and Khmelnitskii. The extracted critical exponents agree with the results obtained by using transfer matrix methods. The necessity of a second parameter is also reflected in the level curvature distribution. Near the critical point the distribution slightly differs from the prediciton of random matrix theory, in agreement with previous works. Close to the quantum Hall fixed points the distribution is lognormal since here states are strongly localized.