Fractional vortex molecules and vortex polygons in a baby Skyrme model

We construct a molecule of fractional vortices with fractional topological lump charges as a baby Skyrmion with the unit topological lump charge in the anti-ferromagnetic (or XY) baby Skyrme model, that is, an O(3) sigma model with a four derivative term and an anti-ferromagnetic or XY-type potential term quadratic in fields. We further construct configurations with topological lump charges Q <= 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 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.