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

@article{Hassaine1998VorticesIT,
  title={Vortices in the Landau--Ginzburg Model of the Quantized Hall Effect},
  author={Mokhtar Hassaine and P. A. Horv'athy and J.-C. Y{\'e}ra},
  journal={Journal of Physics A},
  year={1998},
  volume={31},
  pages={9073-9079}
}
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 common λ→0 limit of two slightly different non-relativistic Maxwell-Chern-Simons models of the type recently introduced by Manton. The equivalence with the model of Zhang, Hansson and Kivelson is demonstrated. 
6 Citations

Figures from this paper

SELF-DUAL VORTICES IN THE FRACTIONAL QUANTUM HALL SYSTEM

Based on the ϕ-mapping theory, we obtain an exact Bogomol'nyi self-dual equation with a topological term, which is ignored in traditional self-dual equation, in the fractional quantum Hall system. It

Lectures on (abelian) Chern-Simons vortices

Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006. Typos

Etude de solitons en th´eorie classique des champs de basse dimension

Cette these porte sur l'analyse de certains modeles de chern-simons en dimension 2 + 1. Partie 1 : par le test de painleve, nous determinons des conditions suffisantes d'integrabilite pour le modele

References

SHOWING 1-10 OF 27 REFERENCES

Multivortex solutions of the Ginzburg-Landau equations

Multivortex solutions of the Ginzburg-Landau equations (or, equivalently, of the Abelian Higgs model) are considered for a special choice of parameters. It is shown that for every n there is a

Nonrelativistic Cherns-Simons theory for the repulsive Bose gas.

We propose a new nonrelativistic Chern-Simons theory based on a simple modification of the standard Lagrangian. This admits asymptotically nonvanishing field configurations and is applicable to the

ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

We prove that a set ofN not necessarily distinct points in the plane determine a unique, real analytic solution to the first order Ginzburg-Landau equations with vortex numberN. This solution has the

First Order Vortex Dynamics

Abstract A non-dissipative model for vortex motion in thin superconductors is considered. The Lagrangian is a Galilean invariant version of the Ginzburg–Landau model for time-dependent fields, with

Non-relativistic Maxwell–Chern–Simons Vortices

Abstract The non-relativistic Maxwell–Chern–Simons model recently introduced by Manton is shown to admit self-dual vortex solutions with non-zero electric field. The interrelated “geometric” and

Effective-field-theory model for the fractional quantum Hall effect.

A field-theory model for the fractional quantum Hall effect and an approximate coarse-grained version of the same model are derived, and a Landau-Ginzburg theory similar to that of Girvin is constructed.

Self-dual Chern-Simons solitons.

These lectures are devoted to the two-year old topic of Chern-Simons solitons, combining the two subjects.

Classical vortex solution of the Abelian Higgs model

An exact vortex solution for the Abelian Higgs model is found when a particular relation between the coupling constants is satisfied. For this case (in which the masses of the scalar and vector

Self-dual anyons in uniform background fields.

  • LeeYi
  • Physics
    Physical review. D, Particles and fields
  • 1995
Various novel self-dual solitons are found in both the symmetric and the asymmetric phases of Chern-Simons-Higgs systems, which satisfy anomalous commutation relations.