Network of edge states: random Josephson junction array description

TL;DR

This paper generalizes the Chalker-Coddington network model to fractional quantum Hall systems, revealing duality symmetries and universality class similarities with disordered Josephson junction arrays, and discusses quantized Hall resistance.

Contribution

It introduces a new network model for fractional quantum Hall effect with duality symmetries and links to Josephson junction arrays, expanding theoretical understanding.

Findings

Model exhibits exact duality symmetries.

Infrared properties match disordered Josephson junction arrays.

Hall resistance is quantized in different regimes.

Abstract

We construct a generalization of the Chalker-Coddington network model to the case of fractional quantum Hall effect, which describes the tunneling between multiple chiral edges. We derive exact local and global duality symmetries of this model, and show that its infrared properties are identical to those of disordered planar Josephson junction array (JJA) in a weak magnetic field, which implies the same universality class. The zero frequency Hall resistance of the system, which was expressed through exact correlators of the tunneling fields, is shown to be quantized both in the quantum Hall limit and in the limit of perfect Hall insulator.