Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

TL;DR

This paper numerically determines the critical index of localization length in a quantum Hall effect model with high precision, providing insights into phase transition behavior.

Contribution

The study introduces a high-precision numerical method for calculating the localization length critical index in the Chalker-Coddington model.

Findings

Critical index ν=2.517±0.018

High-precision Lyapunov exponent calculations

Thorough analysis of finite size effects

Abstract

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.