Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition

TL;DR

This study uses advanced numerical methods to analyze finite size effects and corrections to scaling near the integer quantum Hall transition, leading to more accurate critical exponent estimates.

Contribution

Develops a novel stability analysis method for finite size scaling, improving error estimation and critical exponent determination near IQHT.

Findings

Estimated the irrelevant exponent |y| > 0.4, larger than previous reports.

Confirmed the localization length exponent as 2.62 ± 0.06.

Demonstrated broad applicability of the stability analysis method.

Abstract

We present a numerical finite size scaling study of the localization length in long cylinders near the integer quantum Hall transition (IQHT) employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent $y$ is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate $|y| > 0.4$, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent $2.62 \pm 0.06$ confirming recent results. Our stability analysis has broad applicability to other observables at IQHT, as well as other critical points where corrections to scaling are present.