Effective-action studies of quantum Hall spin textures

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, 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.