Non-relativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries

Abstract

We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in non-relativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) sigma model, a magnetic domain wall in ferromagnets with an easy axis.

13 pages (including Supplemental Material), 1 figure, 3 mpg files (relativistic NG modes for translation and phase, and coupled type-II NG mode), v2: the same text, mpg files added, v3: added discussion on interpolation between relativistic and non-relativistic NG modes, published version