Localization length index in a Chalker-Coddington model: a numerical study

TL;DR

This paper numerically determines the localization length index in the Chalker-Coddington model for quantum Hall transitions, accounting for finite size effects and exploring potential logarithmic corrections.

Contribution

It provides a precise numerical estimate of the localization length index, considering finite size effects and comparing two independent computational approaches.

Findings

Estimated 593 1 0.0297 for 6u in the model.

Two different programs yielded consistent results within error margins.

Logarithmic corrections to finite size effects have larger uncertainties.

Abstract

We calculated numerically the localization length index $\nu$ for the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. By taking into account finite size effects we have obtained $\nu = 2.593 \pm 0.0297$. The calculations were carried out by two different programs that produced close results, each one within the error bars of the other. We also checked the possibility of logarithmic corrections to finite size effects and found, that they come with much larger error bars for $\nu$.