A matrix model for a quantum hall droplet with manifest particle-hole symmetry

TL;DR

This paper introduces a gauged matrix model that naturally exhibits particle-hole symmetry in a quantum Hall droplet, and explores its potential to realize fractional quantum Hall states and edge conformal field theories.

Contribution

It presents a novel matrix model framework for quantum Hall droplets with explicit particle-hole symmetry and discusses possible deformations leading to fractional states and edge theories.

Findings

Matrix model realizes a quantum Hall droplet with particle-hole symmetry.

Deformations can produce two-body potentials for fractional quantum Hall states.

Edge of the droplet exhibits a $c=1/2$ conformal field theory.

Abstract

We find that a gauged matrix model of rectangular fermionic matrices (a matrix version of the fermion harmonic oscillator) realizes a quantum hall droplet with manifest particle-hole symmetry. The droplet consists of free fermions on the topology of a sphere. It is also possible to deform the Hamiltonian by double trace operators, and we argue that this device can produce two body potentials which might lead the system to realize a fractional quantum hall state on the sphere. We also argue that a single gauged fermionic quantum mechanics of hermitian matrices realizes a droplet with an edge that has $c=1/2$ CFT on it.