Scaling Collapse of Longitudinal Conductance near the Integer Quantum Hall Transition

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 Letter, 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 2 orders of magnitude larger than in previous studies. We show numerically that the sizable corrections to scaling of g can be accounted for 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 v = 2.609(7) for the localization length exponent, 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.

Automated summary

This study focuses on the critical properties of the integer quantum Hall transition and suggests using longitudinal conductance as the scaling observable. The authors demonstrate that the corrections to scaling can be accounted for in a simple form, leading to an excellent scaling collapse. They propose a cost-function-based approach and estimate the localization length exponent with high precision. They also confirm their findings using integrated conductance as a scaling variable.