Spontaneous symmetry breaking in open quantum systems: Strong, weak, and strong-to-weak

The authors systematically unravel here the physical consequences of spontaneous symmetry breaking in open quantum systems. They elucidate three scenarios: weak symmetry breaking, which leads to time-crystalline order; strong-to-weak symmetry breaking, which universally generates a gapless Goldstone mode for charge diffusion; and the complete breaking of strong symmetry, characterized by two Goldstone modes that govern order-parameter fluctuations and conserved-charge diffusion, respectively. This work establishes a theoretical framework for characterizing symmetry breaking in open quantum matter.