Driven Phases of Quantum Matter

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Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. By contrast, I will show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases with spontaneously broken symmetries delineated by sharp transitions. Some of these are analogs of equilibrium states, while others are genuinely new to the Floquet setting. I will show that a subset of these novel phases are "time-crystals" in that they spontaneously break the underlying time-translation symmetry of the Floquet drive. Strikingly, the time-crystal phase is remarkably stable to all weak local deformations of the underlying Floquet drives, and the phase simultaneously also spontaneously breaks Hamiltonian dependent emergent spatial symmetries. Thus, the time-crystallinity goes hand in hand with spatial symmetry breaking and, altogether, these phases exhibit a novel form of simultaneous long-range order in space and time. I will describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.