A critical comparison of classical field theory and microscopic wavefunctions for skyrmions in quantum Hall ferromagnets

TL;DR

This paper compares classical field theory and microscopic wavefunctions for skyrmions in quantum Hall ferromagnets, finding the classical approach accurate for larger skyrmions but not for small ones.

Contribution

It provides a systematic validation of the classical non-linear sigma model against microscopic methods for skyrmions in quantum Hall systems.

Findings

Classical field theory is accurate for skyrmions with spin quantum numbers greater than approximately 10.

The classical description fails qualitatively for skyrmions with small spin quantum numbers.

The study bridges microscopic and macroscopic descriptions of skyrmions in quantum Hall ferromagnets.

Abstract

We report on a study of the classical field theory description of charged skyrmions in quantum Hall ferromagnets. The appropriate field theory is a non-linear $\sigma$ model generalized to include Coulomb and Zeeman interaction terms. We have tested the range of validity of the classical field theory by comparing with microscopic descriptions of the single skyrmion state based on the Hartree-Fock approximation, exact diagonalization calculations, and many-body trial wavefunctions. We find that the field theory description is accurate for skyrmions with moderate spin quantum numbers ($\gtrsim 10$) although, as expected, it fails qualitatively for small spin quantum numbers.