Spontaneous breaking of continuous translational invariance

Understand

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.