Discrete Time Crystals and Related Phenomena

Marta P. Estarellas, Tomo Osada, V. M. Bastidas +4 more

Crystals arise as the result of the breaking of a spatial translation symmetry. Similarly, translation symmetries can also be broken in time so that discrete time crystals appear. Here, we introduce a method to describe, characterize, and explore the physical phenomena related to this phase of matter using tools from graph theory. The analysis of the graphs allows to visualizing time-crystalline order and to analyze features of the quantum system. For example, we explore in detail the melting process of a minimal model of a period-2 discrete time crystal and describe it in terms of the evolution of the associated graph structure. We show that during the melting process, the network evolution exhibits an emergent preferential attachment mechanism, directly associated with the existence of scale-free networks. Thus, our strategy allows us to propose a previously unexplored far-reaching application of time crystals as a quantum simulator of complex quantum networks.

Gonzalo Camacho, Benedikt Fauseweh

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 driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.

Norman Y. Yao, Chetan Nayak, Leon Balents +1 more

A. Kyprianidis, J. Zhang, Paul Hess +9 more

Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle

Prethermal discrete time crystals (pDTC) are new collective nonequilibrium phases of matter that break, up to exponentially long times, the discrete time translational symmetry of a periodic drive. Previously studied as a quantum phenomenon, this paper establishes that pDTCs also emerge for classical Hamiltonian dynamics even in their `higher-order and fractional' version. This enables efficient simulations of such phenomena in experimentally relevant settings, including a study of the interplay between dimensionality and interaction range.

J. Zhang, Paul Hess, A. Kyprianidis +9 more