PUB - Publikationen an der Universität Bielefeld

Unbroken continuous translational invariance is often taken as a basicassumption in discussions of spontaneous symmetry breaking (SSB), which singlesout SSB of translational invariance itself as an exceptional case. We present aframework which allows us to treat translational invariance on the same footingas other symmetries. It is shown that existing theorems on SSB can bestraightforwardly extended to this general case. As a concrete application, weanalyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove onthe ground of the general theorems that the Bogoliubov mode stemming from aspontaneously broken internal U(1) symmetry and the longitudinal phonon due toa crystalline order are distinct physical modes.