Scaling collapse of longitudinal conductance near the integer quantum Hall transition

TL;DR

This study improves the understanding of the integer quantum Hall transition by analyzing longitudinal conductance at larger system sizes, revealing a Gaussian scaling function and providing a more precise critical exponent estimate.

Contribution

The paper introduces a new approach using longitudinal conductance as the scaling observable, enabling better scaling collapse and more accurate critical exponent estimation.

Findings

Scaling corrections can be effectively modeled in a simple form.

The scaling function is indistinguishable from a Gaussian.

Critical exponent ν is estimated as 2.607(8).

Abstract

Within the mature field of Anderson transitions, the critical properties of the integer quantum Hall transition still pose a significant challenge. Numerical studies of the transition suffer from strong corrections to scaling for most observables. In this work, we suggest to overcome this problem by using the longitudinal conductance $g$ of the network model as the scaling observable, which we compute for system sizes nearly two orders of magnitude larger than in previous studies. We show numerically that the sizeable corrections to scaling of $g$ can be included in a remarkably simple form which leads to an excellent scaling collapse. Surprisingly, the scaling function turns out to be indistinguishable from a Gaussian. We propose a cost-function-based approach, and estimate $\nu=2.607(8)$, consistent with previous results, but considerably more precise than in most works on this problem. Extending previous approaches for Hamiltonian models, we also confirm our finding using integrated conductance as a scaling variable.