The Quantum Hall Effect in Supersymmetric Chern-Simons Theories

TL;DR

This paper introduces a supersymmetric Chern-Simons theory modeling the fractional quantum Hall effect, enabling analytical solutions and revealing that vortex excitations exhibit fractional charge and spin.

Contribution

It presents an analytically solvable supersymmetric Chern-Simons model that reproduces key features of the fractional quantum Hall effect, including vortex excitations with fractional quantum numbers.

Findings

Vortex ground state wavefunction matches Laughlin state universality class

Constructed coherent states for vortex excitations

Demonstrated fractional charge and spin of quasi-holes

Abstract

We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics to a matrix model, show that their ground state wavefunction is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.