Corrections to Scaling in the Integer Quantum Hall Effect

TL;DR

This paper investigates finite size corrections to scaling laws in the integer quantum Hall effect, showing that these corrections can explain apparent non-universality and supporting the universality of the localization length exponent across different conditions.

Contribution

The study provides a systematic numerical analysis of finite size corrections, demonstrating their role in the apparent non-universality of the localization length exponent in the quantum Hall effect.

Findings

Irrelevant scaling index y_irr = -0.38 ± 0.04 in the second Landau level

Additional periodic potential is irrelevant with the same scaling index in the lowest Landau level

Results support the universality of the localization length exponent ν across Landau levels and potentials

Abstract

Finite size corrections to scaling laws in the centers of Landau levels are studied systematically by numerical calculations. The corrections can account for the apparent non-universality of the localization length exponent $\nu{}$. In the second lowest Landau level the irrelevant scaling index is $y_{\mathrm{irr}}=-0.38\pm0.04$. At the center of the lowest Landau level an additional periodic potential is found to be irrelevant with the same scaling index. These results suggest that the localization length exponent $\nu$ is universal with respect to Landau level index and an additional periodic potential.