A Matrix Model for Non-Abelian Quantum Hall States

TL;DR

This paper introduces a matrix quantum mechanics model for non-Abelian quantum Hall states with internal SU(p) spins, connecting vortex quantization, Chern-Simons theory, and boundary WZW models to describe complex quantum states.

Contribution

It presents a novel matrix model for non-Abelian quantum Hall states, linking it to Chern-Simons and WZW theories, and generalizing known states like Moore-Read.

Findings

Matrix model describes non-Abelian quantum Hall states with SU(p) spins

Ground states include spin-singlet Moore-Read and Read-Rezayi states

Model derived from vortex quantization in Chern-Simons theory

Abstract

We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU(p) spin. The ground states of the matrix model include spin-singlet generalisations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a U(p) Chern-Simons theory. We show how the matrix model can be derived from quantisation of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.