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Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in…
Continuous time crystal (CTC) and quasi-crystal (CTQC) are two novel phases of matter characterized by the spontaneous breaking of continuous time-translation symmetry. To date, realizations of CTCs with periodic oscillations have been…
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…
Continuous time crystals, i.e., nonequilibrium phases with a spontaneously broken continuous time-translational symmetry, have been studied and recently observed in the long-time dynamics of open quantum systems. Here, we investigate a…
Continuous time crystals (CTCs) - media with broken continuous time translation symmetry - are an eagerly sought state of matter that spontaneously transition from a time-independent state to one of periodic motion in response to a small…
Spontaneous symmetry breaking plays a pivotal role in physics ranging from the emergence of elementary particles to the phase transitions of matter. The spontaneous breaking of continuous time translation symmetry leads to a novel state of…
Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time.…
We investigate the emergence of time quasicrystals (TQCs) in the open Dicke model, subjected to a quasi-periodic Fibonacci drive. TQCs are characterized by a robust sub-harmonic quasi-periodic response that is qualitatively distinct from…
A quantum phase of matter can be understood from the symmetry of the system's Hamiltonian. The system symmetry along the time axis has been proposed to show a new phase of matter referred as discrete-time crystals (DTCs). A DTC is a quantum…
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…
The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay…
Time quasicrystals (TQCs) represent a compelling extension of the concept of time crystals (TCs). While TCs break discrete time-translation symmetry by exhibiting a periodic response at a subharmonic of the driving frequency, TQCs display a…
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…
Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external…
Exploring continuous time crystals (CTCs) within the symmetric subspace of spin systems has been a subject of intensive research in recent times. Thus far, the stability of the time-crystal phase outside the symmetric subspace in such spin…
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 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…
Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of…
Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation…