Related papers: Quantum Time Crystals from Hamiltonians with Long-…
Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we…
In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and…
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation…
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…
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…
Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…
Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not…
Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles…
We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
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.…
Time crystals appear when systems display a commensurate spontaneous breaking of the discrete time translational invariance imposed by an external periodic drive. No consensus on the definition has been reached as yet, but important aspects…
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…
A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. DTCs promise profound applications in precision time-keeping and other…
In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…
Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the…
Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…
The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet,…
In this work we introduce {\it boundary time-crystals}. Here {\it continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we…