### Abstract

We propose color magnetism as a generalization of the ordinary Heisenberg (anti-)ferro magnets on a triangular lattice. Vortex matter consisting of an Abrikosov lattice of non-Abelian vortices with color magnetic fluxes shows a color ferro or anti-ferro magnetism, depending on the interaction among the vortex sites. A prime example is a non-Abelian vortex lattice in rotating dense quark matter, showing a color ferromagnetism. We show that the low-energy effective theory for the vortex lattice system in the color ferromagnetic phase is described by a 3+1 dimensional CP ^{N -1} nonlinear sigma model with spatially anisotropic couplings. We identify gapless excitations independent from Tkachenko modes as color magnons, that is, Nambu-Goldstone modes propagating in the vortex lattice with an anisotropic linear dispersion relation ω_{p} ^{2} = c_{xy} ^{2}c(p _{x} ^{2} + p_{y} ^{2}) + c_{z} ^{2} p _{z} ^{2}. We calculate the transition temperature between the ordered and disordered phases, and apply it to dense quark matter. We also identify the order parameter spaces for color anti-ferromagnets.

Original language | English |
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Article number | 130 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2014 Jun 1 |

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### Keywords

- Sigma Models
- Solitons Monopoles and Instantons
- Spontaneous Symmetry Breaking
- Topological States of Matter

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2014*(6), [130]. https://doi.org/10.1007/JHEP06(2014)130