A Smörgåsbord of Skyrmions

Author:

Gudnason Sven BjarkeORCID,Halcrow Chris

Abstract

Abstract We study static solutions of the standard Skyrme model with a pion mass. Using approximately 105 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 D2d symmetric fullerene or a new C2v 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.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

Cited by 12 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Modified sine-Gordon theory with static multikinks;Physical Review D;2024-09-13

2. Nonlinear rigid-body quantization of Skyrmions;Physical Review D;2024-06-03

3. Quantum binding energies in the Skyrme model;Physics Letters B;2024-03

4. Nudged Elastic Bands and Lightly Bound Skyrmions;Symmetry, Integrability and Geometry: Methods and Applications;2023-10-11

5. Asymptotic states for kink–meson scattering;The European Physical Journal C;2023-08-22

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