Quantum synchronization via weak symmetry breaking.*

Symmetries of a microscopic Hamiltonian strongly constrain both the thermodynamics and dynamics of isolated systems in thermal equilibrium. Far from equilibrium however, the role of symmetry in determining local dynamics is not universally understood. To this end, we uncover a mechanism that yields synchronized relaxation of local observables mediated by a weakly broken, continuous symmetry. We provide a family of strongly interacting spin models which exemplify this phenomenon, including a quantum generalization of the Kuramoto model, whose classical synchronization transition is well studied. Remarkably, signatures of this phenomena are visible even when restricting to global measurement, making our theory relevant to a diverse set of quantum systems ranging from ensembles of nitrogen vacancy centers in diamond to reconfigurable atom arrays. Finally, we give evidence that these collective dynamics generate metrologically useful states, even in systems where the preparation of spin squeezed states is precluded.