Strong-to-Weak Spontaneous Symmetry Breaking of Dephased Fermions

Strong-to-weak spontaneous symmetry breaking (SWSSB) is a novel phase transition in mixed states associated with the loss of global charge information. In this work we study fermions with U(1) symmetry under infinite density dephasing and derive the SWSSB properties of the resulting mixed states. Our central observation is that at infinite dephasing every Renyi correlator is exactly the spin-spin correlator of a compact XY model, whose Boltzmann weight is the squared full-counting-statistics generating function of a classical ensemble built from the parent state. For the Renyi-2 correlator it is the full counting statistics of the parent state itself. We complement the infinite dephasing mapping with a novel diagrammatic expansion for the Renyi-1 correlator, applicable to any diagonal mixed state, which computes the couplings of the Renyi-1 XY model. We also study a replica field theory for even Renyi index quantities, applicable at finite dephasing. Our analysis indicates that fully dephased metals display long-range SWSSB in d at least 2, as confirmed numerically and experimentally in d=2, and quasi-long-range SWSSB in d=1. For insulating parent states both an SWSSB and a trivial phase are possible at infinite dephasing depending on UV details. Long-range SWSSB in d at least 3, or quasi-long-range SWSSB in d=2, survives above a nonuniversal, Renyi-index-dependent threshold and is lost when the parent state is deep in the insulating phase, with the exception of quantum Hall insulators which generically have quasi-long-range SWSSB. For even Renyi indices we also determine the stability of the SWSSB phase away from infinite dephasing and derive the universality class of the SWSSB transition.