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arXiv · 1403.4031

Non-relativistic Nambu-Goldstone modes propagating along a skyrmion line

Michikazu Kobayashi·Muneto Nitta
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Abstract

We study Nambu-Goldstone (NG) modes or gapless modes propagating along a skyrmion (lump) line in a relativistic and non-relativistic O(3) sigma model, the latter of which describes isotropic Heisenberg ferromagnets. We show for the non-relativistic case that there appear two coupled gapless modes with a quadratic dispersion. In addition to the well-known Kelvin mode consisting of two translational zero modes transverse to the skyrmion line, we show that the other consists of a magnon and dilaton, that is, a NG mode for a spontaneously broken internal U(1) symmetry and a quasi-NG mode for a spontaneously broken scale symmetry of the equation of motion. We find that the commutation relations of Noether charges admit a central extension between the dilatation and phase rotation, in addition to the one between two translations found recently. The counting rule is consistent with the Nielsen-Chadha and Watanabe-Brauner relations only when we take into account quasi-NG modes.

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BibTeXRIS

Michikazu Kobayashi, Muneto Nitta. 2014-07-11. Non-relativistic Nambu-Goldstone modes propagating along a skyrmion line. https://doi.org/10.1103/physrevd.90.025010

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