The spontaneous breaking of time-translation symmetry has led to the discovery of a new
phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic …

Dissipative time crystals can appear in spin systems, when the Z 2 symmetry of the
Hamiltonian is broken by the environment, and the square of total spin operator S 2 is …

Higher-order and fractional discrete time crystals (DTCs) are exotic phases of matter where
the discrete time translation symmetry is broken into higher-order and non-integer category …

Systems subject to a high-frequency drive can spend an exponentially long time in a
prethermal regime, in which novel phases of matter with no equilibrium counterpart can be …

A time crystal is an exotic phase of matter where time-translational symmetry is broken; this
phase differs from the spatial symmetry breaking induced in conventional crystals. Lots of …

The breaking of the continuous time-translation symmetry manifests, in Markovian open
quantum systems, through the emergence of nonstationary dynamical phases. Systems that …

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-
body systems can host nonequilibrium phases of matter. In particular, we show that there …

The existence of multistability in quantum systems beyond the mean-field approximation
remains an intensely debated open question. Quantum fluctuations are finite-size …

Discrete time crystals are novel phases of matter that break the discrete time translational
symmetry of a periodically driven system. In this Letter, we propose a classical system of …

Crystal seeding enables a deeper understanding of phase behavior, leading to the
development of methods for controlling and manipulating phase transitions in various …