Quantum Hall states as matrix Chern-Simons theory

TL;DR

This paper introduces a matrix Chern-Simons model to describe finite quantum Hall fluids, demonstrating quantum mechanical quantization consistent with Laughlin theory and linking it to the Calogero model.

Contribution

It presents a novel finite matrix Chern-Simons model for quantum Hall states, establishing its quantization properties and equivalence to the Calogero model.

Findings

Quantization of inverse filling fraction matches Laughlin theory

Model effectively describes finite quantum Hall fluids

Establishes equivalence with Calogero model

Abstract

We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the quasiparticle number is shown to arise quantum mechanically and to agree with Laughlin theory. We also point out the effective equivalence of this model, and therefore of the quantum Hall system, with the Calogero model.