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The study of topologically ordered states have given rise to a growing interest in symmetry protected states in quantum matter. Recently, this theory has been extended to quantum many body systems which demonstrate ordered states at low…
Here we provide a theoretical framework to analyze discrete time-crystalline phases (DTC) in open quantum many-body systems. As a particular realization, we choose a quantum many-body system that exhibits cascaded prethermalization . The…
Many-body quantum systems, under suitable conditions, exhibit time-translation symmetry breaking and settle in a discrete time crystalline (DTC) phase -- an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust…
Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry.…
Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with $nT$ periodicity under a $T$-periodic Hamiltonian, where $n>1$ is an integer insensitive to small parameter variations. In…
The discrete time crystal (DTC) is a recently discovered phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body-localization is required to stabilize a DTC to arbitrary times, yet an experimental…
Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We…
We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal…
Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent…
Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase…
Discrete time crystals (DTCs) are novel out-of-equilibrium quantum states of matter which break time translational symmetry. DTCs have been extensively realized in experiments, particularly their subclass that is characterized by…
Discrete time crystals (DTC) exhibit a special non-equilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization…
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and…
Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, with potential applications ranging from quantum computing to sensing and metrology. There has been significant recent interest in…
Novel dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be…
Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under…
Persistent oscillatory dynamics in non-equilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time…
A remarkable consequence of spontaneously breaking the time translational symmetry in a system, is the emergence of time crystals. In periodically driven systems, discrete time crystals (DTC) can be realized which have a periodicity that is…
The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the…
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized…