TL;DR
This paper explores triply-periodic solutions in generalized Skyrme models with squashed 3-sphere target spaces, revealing new crystal structures and configurations beyond the standard cubic lattice.
Contribution
It introduces a family of Skyrme systems with varying target space geometries and identifies novel minimal-energy crystal solutions in these models.
Findings
Standard Skyrme model has a cubic lattice of half-skyrmions as lowest-energy crystal.
Squashed Skyrme models exhibit different minimal-energy crystal structures.
New solutions include vortex arrays and multi-sheeted configurations.
Abstract
This letter deals with triply-periodic (crystalline) solutions in a family of Skyrme systems, namely where the field takes values in the squashed 3-sphere. The family includes the standard Skyrme model (round 3-sphere), and the Skyrme-Faddeev case (maximal squashing). In the round case, the lowest-energy crystal is the well-known cubic lattice of half-skyrmions; but in the squashed case the minimal-energy crystal structures turn out to be different. We describe some of the solutions that arise, including arrays of vortices and multi-sheeted structures.
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