Routes to maximize the lifetime of discrete time crystals*

Motivated by the recent observation of time crystals in the absence of disorder, we propose schemes to extend the lifetime of a discrete time crystal in a translation invariant Ising spin chain. We derive an analytical framework to show that by appropriately tuning the interactions, it is always possible to observe time crystal signatures in a finite size chain. We also obtain an expression for the optimal value of the Ising interaction that maximizes the lifetime of the time crystal. Our results hold for both short and long range interacting systems. Furthermore, we find that in the thermodynamic limit, only an infinite range interaction can lead to a time crystal in the absence of disorder. Our work elucidates the crucial role of interactions in realizing a time crystal.