Fractional quantum Hall effect on the two-sphere: a matrix model proposal

TL;DR

This paper proposes a Chern-Simons matrix model for the fractional quantum Hall effect on a two-sphere, linking it to the Calogero-Sutherland model and Haldane wavefunctions, providing a new theoretical framework.

Contribution

It introduces a novel matrix model approach for the fractional quantum Hall effect on the sphere, establishing its equivalence to known models and wavefunctions.

Findings

Reproduces quantum states and filling fractions

Shows equivalence to Calogero-Sutherland model restrictions

Aligns with Haldane spherical wavefunctions

Abstract

We present a Chern-Simons matrix model describing the fractional quantum Hall effect on the two-sphere. We demonstrate the equivalence of our proposal to particular restrictions of the Calogero-Sutherland model, reproduce the quantum states and filling fraction and show the compatibility of our result with the Haldane spherical wavefunctions.