Fractional vortex molecules and vortex polygons in a baby Skyrme model

Abstract

We construct a molecule of fractional vortices with fractional topological lump charges as a baby Skyrmion with the unit topological lump charge in the antiferromagnetic (or XY) baby Skyrme model, that is, an $O(3)$ sigma model with a four-derivative term and an antiferromagnetic or XY-type potential term quadratic in fields. We further construct configurations with topological lump charges $Q\ensuremath{\le}7$ and find that bound states of vortex molecules constitute regular polygons with $2Q$ vertices as vortices, where the rotational symmetry $SO(2)$ in real space is spontaneously broken into a discrete subgroup ${\mathbf{Z}}_{Q}$. We also find metastable and arrayed bound states of fractional vortices for $Q=5$, 6. On the other hand, we find for $Q=7$ that the regular polygon is metastable and the arrayed bound state is stable. We calculate binding energies of all configurations.