Spontaneous breaking of continuous translational invariance
arXiv:1112.3890 · doi:10.1103/PhysRevD.85.085010
Abstract
Unbroken continuous translational invariance is often taken as a basic assumption in discussions of spontaneous symmetry breaking (SSB), which singles out SSB of translational invariance itself as an exceptional case. We present a framework which allows us to treat translational invariance on the same footing as other symmetries. It is shown that existing theorems on SSB can be straightforwardly extended to this general case. As a concrete application, we analyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove on the ground of the general theorems that the Bogoliubov mode stemming from a spontaneously broken internal U(1) symmetry and the longitudinal phonon due to a crystalline order are distinct physical modes.
14 pages, 4 pdf/jpg figures, REVTeX 4.1; v2: section IV expanded, new appendix and references added, numerous other minor modifications throughout the text
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