Localization length exponent in two models of quantum Hall plateau transitions

TL;DR

This study re-evaluates the critical localization length exponent in quantum Hall transitions using continuum and lattice models, finding results consistent with earlier models but differing from recent network model studies.

Contribution

It provides a refined calculation of the localization length exponent in quantum Hall models, clarifying discrepancies with recent network model findings.

Findings

Exponent $ u$ = 2.48 ± 0.02 consistent with earlier models

Irrelevant length scale exponent y = 4.3 in lattice model

Irrelevant perturbations negligible in topology calculations

Abstract

Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the exponent calculation in the continuum model and in the lattice model, both projected to the lowest Landau level or subband. Combining scaling results with or without the corrections of an irrelevant length scale, we obtain $\nu = 2.48 \pm 0.02$, which is larger but still consistent with the earlier results in the two models, unlike what was found recently in the network model. The scaling of the total number of conducting states, as determined by the Chern number calculation, is accompanied by an effective irrelevant length scale exponent $y = 4.3$ in the lattice model, indicating that the irrelevant perturbations are insignificant in the topology number calculation.