Localization Properties of the Chalker-Coddington Model

TL;DR

This paper analyzes the Chalker-Coddington model, demonstrating finite localization length, spectral localization, and deriving a Thouless formula, thereby advancing understanding of quantum Hall effect transitions.

Contribution

It provides rigorous proofs of Lyapunov exponent simplicity, finite localization length, and spectral localization for the model, along with a Thouless formula derivation.

Findings

Lyapunov exponents are simple

Localization length is finite

Spectral localization is established

Abstract

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.