On the theory of plateau-plateau transitions in Quantum Hall Effect

TL;DR

This paper develops a Lagrangian formulation for the Chalker-Coddington network model of quantum Hall plateau transitions, revealing its integrability and potential for exact analysis using Algebraic Bethe Ansatz.

Contribution

It introduces a Lagrangian framework for the model on Manhattan Lattice and demonstrates its integrability, enabling exact solutions for quantum Hall transition physics.

Findings

Model is integrable via Algebraic Bethe Ansatz

Lagrangian formulation derived for the network model

Potential for exact analysis of plateau transitions

Abstract

The Lagrangian (action) formulation of the Chalker-Coddington network model for plateau-plateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice ($ML$). The dimensionless Landauer resistance is considered and its average is calculated over the random U(1) phases with constant distribution on the circle. The Lagrangian of the resultant model on $ML$ is found and the corresponding $R$-matrix is written down. It appeared, that this model is integrable, rising hope to investigate physics of plateau- plateau transitions by the exact method of powerful Algebraic Bethe Ansatz $(ABA)$.