Lattices of Generalized Skyrmions

Abstract

Generalized Skyrme systems are those which include both the Skyrme and the Skyrme-Faddeev models through an interpolating parameter \alpha \in [0,1] the former corresponds to \alpha=0 and the latter to \alpha=1. Our numerical and analytical investigations centre around the \alpha=0 Skyrme crystal, its deformations, and its behaviour and symmetries as a function of \alpha, called the generalized Skyrme crystal. We show that a double square lattice emerges when the Skyrme crystal is deformed in a certain limit; we compare its energy with the one corresponding to a double hexagonal lattice and show that it has a lower energy-per-charge than its hexagonal counterpart. On the other hand, vortex-like structures with two 1-vortices (vortices of order 1) and two 1-antivortices, denoted V+AV+V+AV, appear when the Skyrme crystal is deformed in a different limit, as well as when the generalized Skyrme crystal is taken close to the Skyrme-Faddeev limit. This leads us to the study of generalized V+AV and V+AV+V+AV configurations, as a function of \alpha. We show that when these configurations are stacked in the axial direction, they exhibit some winding and linking properties as they are taken close to the Skyrme-Faddeev limit, where the V+AV+V+AV configurations appear to be more stable than their V+AV counterparts. Finally, the study of such configurations led to the discovery of two crystalline solutions whose properties are investigated in some detail: a 2-vortex/2-antivortex pair, denoted 2V+2AV, and a “multi-sheet” solution, both of which have a lower energy-per-charge than the V+AV+V+AV solution, in the Skyrme-Faddeev limit