Integer quantum Hall transition on a tight-binding lattice

TL;DR

This paper investigates the critical behavior of the integer quantum Hall transition using a microscopic disordered electron model, confirming the localization length exponent aligns with the Chalker-Coddington network results, thus addressing longstanding discrepancies.

Contribution

It provides high-accuracy numerical evidence supporting the Chalker-Coddington model's predictions for the localization length exponent in the quantum Hall transition.

Findings

Localization length exponent ν=2.58(3) confirmed

Supports the validity of the Chalker-Coddington network model

Addresses discrepancies in theoretical and experimental results

Abstract

Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ significantly from each other, casting doubt on our fundamental understanding. While this discrepancy is often attributed to long-range Coulomb interactions, Gruzberg et al. [Phys. Rev. B 95, 125414 (2017)] recently suggested that the semiclassical Chalker-Coddington model, widely employed in numerical simulations, is incomplete, questioning the established central theoretical results. To shed light on the controversy, we perform a high-accuracy study of the integer quantum Hall transition for a microscopic model of disordered electrons. We find a localization length exponent $\nu=2.58(3)$ validating the result of the Chalker-Coddington network.