The baby Skyrme models and their multi-skyrmions

TL;DR

This paper investigates the structure and stability of multi-skyrmion solutions in baby Skyrme models, revealing that certain potentials lead to radially symmetric, tightly bound multi-skyrmions with linear energy growth, contrasting previous models.

Contribution

It demonstrates that a baby Skyrme model with a two-vacua potential produces stable, radially symmetric multi-skyrmions with linear energy scaling, a novel finding in the field.

Findings

Multi-skyrmions are radially symmetric in the two-vacua model.

Energy of multi-skyrmions grows linearly with topological charge n.

Multi-skyrmions are more tightly bound and energetically favorable than in single-vacuum models.

Abstract

We study the structure of minimal-energy solutions of the baby Skyrme models for any topological charge n; the baby multi-skyrmions. Unlike in the (3+1)D nuclear Skyrme model, a potential term must be present in the (2+1)D Skyrme model to ensure stability. The form of this potential term has a crucial effect on the existence and structure of baby multi-skyrmions. The simplest holomorphic model has no known stable minimal-energy solution for n greater than one. The other baby Skyrme model studied in the literature possesses non-radially symmetric minimal-energy configurations that look like `skyrmion lattices' formed by skyrmions with n=2. We discuss a baby Skyrme model with a potential that has two vacua. Surprisingly, the minimal-energy solution for every n is radially-symmetric and the energy grows linearly for large n. Further, these multi-skyrmions are tighter bound, have less energy and the same large r behaviour than in the model with one vacuum. We rely on numerical studies and approximations to test and verify this observation.