Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory

TL;DR

This paper introduces a unitary matrix Chern-Simons model for fractional quantum Hall states on a finite cylinder, reproducing key Laughlin properties and linking to an integrable particle system.

Contribution

It presents a novel matrix model that captures fractional quantum Hall physics on a cylinder and establishes a holographic connection to the Sutherland model.

Findings

Reproduces quantization of inverse filling fraction

Models quasiparticle number quantization

Links to Sutherland integrable system

Abstract

We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the quantization of the inverse filling fraction and of the quasiparticle number, are reproduced by the quantum mechanics of the matrix model. We also point out that this system is holographically described in terms of the one-dimensional Sutherland integrable particle system.