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We report on a study of the classical field theory description of chargedskyrmions in quantum Hall ferromagnets. The appropriate field theory is anon-linear $\sigma$ model generalized to include Coulomb and Zeeman interactionterms. We have tested the range of validity of the classical field theory bycomparing with microscopic descriptions of the single skyrmion state based onthe Hartree-Fock approximation, exact diagonalization calculations, andmany-body trial wavefunctions. We find that the field theory description isaccurate for skyrmions with moderate spin quantum numbers ($\gtrsim 10$)although, as expected, it fails qualitatively for small spin quantum numbers.Comment: 10 page

Critical comparison of classical field theory and microscopic wave functions for skyrmions in quantum Hall ferromagnets