Vortices in the Landau--Ginzburg Model of the Quantized Hall Effect

TL;DR

This paper demonstrates that the Landau--Ginzburg model for the Quantum Hall Effect admits stable vortex solutions, connecting it to Maxwell--Chern--Simons models and the Zhang-Hansson-Kivelson framework.

Contribution

It shows the existence of stable vortex solutions in a modified Landau--Ginzburg model and establishes its equivalence with a known Maxwell--Chern--Simons model.

Findings

Stable topological and non-topological vortices identified.

Equivalence with Zhang-Hansson-Kivelson model demonstrated.

Connection to Maxwell--Chern--Simons models established.

Abstract

The `Landau--Ginzburg' theory of Girvin and MacDonald, modified by adding the natural magnetic term, is shown to admit stable topological as well as non-topological vortex solutions. The system is the commun $\lambda\to0$ limit of two slightly different non-relativistic Maxwell--Chern--Simons models of the type introduced recently by Manton. The equivalence with the model of Zhang, Hansson and Kivelson is demonstrated.