A Smörgåsbord of Skyrmions

Abstract: We study static solutions of the standard Skyrme model with a pion mass. Using approximately $10^5$ pseudo-random initial configurations made of single Skyrmions in the non-symmetrized product Ansatz and an automatic detection of repeated solutions, we find 409 local energy minimizers (Skyrmions) of the model with baryon numbers 1 through 16, of which 383 are new. In particular, we find new solutions for baryon numbers 5, 8, 9, 10, 11, 12, 13, 14, 15, and 16. Our results for the number of solutions per baryon number suggest that this number could grow either polynomially or exponentially. We identify new families of solutions: sheets of Skyrmions in synchronized and antisynchronized hexagonal layers (which we call graphene); chains of 2- and 3-tori; chain-like solutions containing a hinge and many clustered Skyrmions. Contrary to common lore, only the $B=12$ global energy minimizer is made of alpha particles or some chunk of a cubic crystal, whereas the $B=9,11,14,15$ minimizers contain the $B=7$ icosahedrally symmetric Skyrmion as a component. The $B=10,13,16$ are symmetric graphene-like solutions. We find $B=5$ and $B=8$ minimizers with numerically indistinguishable energies. The $B=8$ candidates are the chain of two cubes, which is a chunk of the cubic Skyrme crystal and the fullerene-type ball found originally by the rational map approximation. The $B=5$ global minimizer is either the well-known $D_{2d}$ symmetric fullerene or a new $C_{2v}$ symmetric solution. Finally, our findings show a large number of solutions have no discrete symmetries or just one symmetry, contrary to the common lore that Skyrmions are highly symmetric configurations.