A Long Range, Pre-thermal Time Crystal in One Dimension

Periodically driven (Floquet) systems provide an ideal platform for exploring out-of-equilibrium dynamics. In this talk, we present the numerical observation of time crystalline order in a prethermal one dimensional spin chain with long range interactions. We demonstrate that power-law interactions, with exponent α < 2, are essential to stabilize such order in 1D. In particular, we compare to the case of short-range interactions, where a robust prethermal regime is also observed, but where the time-crystalline order decays rapidly. Finally, we examine the dynamics of domain walls in the long-range system and discuss recent experiments in trapped ions.