Irrelevant Corrections at the Quantum Hall Transition

The quantum Hall effect is one of the most extensively studied topological effects in solid-state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous numerical finite size scaling studies have focused on the critical exponent nu for the correlation length. In such studies, it is important to take proper account of irrelevant corrections to scaling. Recently, Dresselhaus et al. proposed a new scaling ansatz, which they applied to the two terminal conductance of the Chalker-Coddington model. Herein, their proposal is applied to the previously reported data for the Lyapunov exponents of that model using both polynomial fitting and Gaussian process fitting.

Automated summary

The quantum Hall effect is extensively studied in solid-state physics and exhibits critical phenomena described by universal critical exponents. Finite size scaling studies have focused on the correlation length critical exponent nu, and it is important to consider irrelevant corrections to scaling. Recently, Dresselhaus et al. proposed a new scaling ansatz applied to the two terminal conductance of the Chalker-Coddington model. In this study, their proposal is applied to previously reported data for the Lyapunov exponents of that model using polynomial fitting and Gaussian process fitting.