Effective Action Studies of Quantum Hall Spin Textures

TL;DR

This paper combines analytic and numerical methods to study spin textures, especially skyrmions, in quantum Hall systems, providing new solutions, energy estimates, and edge texture descriptions within an effective action framework.

Contribution

It introduces approximate analytic solutions for skyrmions of arbitrary charge and a numerical technique for profile determination, advancing understanding of quantum Hall spin textures.

Findings

Analytic solutions for skyrmions of arbitrary charge

Numerical profiles agree with analytic and Hartree-Fock results

Edge textures are characterized within the effective action approach

Abstract

We report on analytic and numerical studies of spin textures in quantum Hall systems using a long-wavelength effective action for the magnetic degrees of freedom derived previously. The majority of our results concern skyrmions or solitons of this action. We have constructed approximate analytic solutions for skyrmions of arbitrary topological and electric charge and derived expressions for their energies and charge and spin radii. We describe a combined shooting/relaxational technique for numerical determination of the skyrmion profiles and present results that compare favorably with the analytic treatment as well as with Hartree-Fock studies of these objects. In addition, we describe a treatment of textures at the edges of quantum Hall systems within this approach and provide details not reported previously.