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.

arXiv commentLaTeX: 28 + 77 pages, 16 figures and 16 tables, animations of all solutions rotating at http://bjarke.gudnason.net/smoergaasbord; V2: comments added, reference added and typos corrected

References in corpus (33)

• Rational Maps, Monopoles and Skyrmions
• A Skyrme-type proposal for baryonic matter
• Symmetric Skyrmions
• Skyrmions, instantons and holography
• Skyrmions, Fullerenes and Rational Maps
• Skyrmions with low binding energies
• Skyrmions with massive pions
• Skyrmions in a truncated BPS theory
• Skyrmions and the pion mass
• Solitonic fullerene structures in light atomic nuclei
• Light Nuclei as Quantized Skyrmions
• A dynamical $\alpha$-cluster model of ${}^{16}$O
• Skyrmions and clustering in light nuclei
• States of Carbon-12 in the Skyrme Model
• Skyrmions up to Baryon Number 108
• Topological energy bounds for the Skyrme and Faddeev models with massive pions
• Vibrational quantisation of the B=7 Skyrmion
• A Skyrme lattice with hexagonal symmetry
• Loosening up the Skyrme model
• Topological energy bounds in generalized Skyrme models
• A point particle model of lightly bound skyrmions
• Vibrational modes of Skyrmions
• Chains of Skyrmions
• The volume of a soliton
• Exploring the generalized loosely bound Skyrme model
• Oxygen-16 Spectrum from Tetrahedral Vibrations and their Rotational Excitations
• Realistic classical binding energies in the $\omega$-Skyrme model
• Classical Skyrmions -- Static Solutions and Dynamics
• Magnetic Bags and Black Holes
• ADHM skyrmions
• Skyrmion Multi-Walls
• Evidence for Tetrahedral Structure of Calcium-40
• A BPS Skyrme model

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