An accurate effective action for `baby' to `adult' skyrmions

TL;DR

This paper derives a comprehensive effective action for quantum Hall skyrmions from Chern-Simons theory, accurately capturing their static profiles and energies across various sizes, aligning well with microscopic calculations and simplifying the understanding of their physics.

Contribution

It introduces a new effective classical model for skyrmions that incorporates both large- and short-distance physics, matching microscopic results.

Findings

Classical skyrmion profiles agree with microscopic calculations.

Skyrmion energies follow the Sondhi et al. formula across parameters.

Continuum classical models can effectively describe skyrmion physics.

Abstract

Starting with a Chern-Simons theory, we derive an effective action for interacting quantum Hall skyrmions that takes into account both large-distance physics and short-distance details as well. We numerically calculate the classical static skyrmion profile from this action and find excellent agreement with other, microscopic calculations over a wide range of skyrmion sizes including the experimentally relevant one. This implies that the essential physics of this regime might be captured by a continuum classical model rather than resorting to more microscopic approaches. We also show that the skyrmion energy closely follows the formula suggested earlier by Sondhi et al. for a broad parameter range of interest as well.