Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect

TL;DR

This paper investigates hierarchical network models for the quantum Hall effect, analyzing their localization transition, conductance distribution, and multifractal properties to understand critical phenomena.

Contribution

It introduces a recursive hierarchical model for the quantum Hall effect and numerically determines key critical exponents and distributions.

Findings

Critical conductance distribution calculated

Localization length exponent determined

Multifractal exponents of eigenstates obtained

Abstract

We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.