Spontaneous breaking of continuous translational invariance

Details Spontaneous breaking of continuous translational invariance Spontaneous breaking of continuous translational invariance

2011-12-16

arxiv.org/abs/1112.3890v2

Phys.Rev.D85:085010,2012

Physics

Condensed Matter

Statistical Mechanics

14 pages, 4 pdf/jpg figures, REVTeX 4.1; v2: section IV expanded, new appendix and references added, numerous other minor modi

Scientific paper

10.1103/PhysRevD.85.085010

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.

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