Bridging closed and dissipative discrete time crystals in spin systems with infinite-range interactions

Abstract

We elucidate the role of dissipation on the emergence of time crystals in a periodically driven spin system with infinite-range interactions. By mapping out the phase diagrams for varying dissipation strengths, ranging from zero to infinitely strong, we demonstrate that the area in the phase diagram, where a time crystal exists, grows with the dissipation strength, but only up to an optimal point, beyond which most of the time crystals become unstable. We find signatures of time crystalline phases in both closed-system and dissipative regimes under the right conditions. However, the dissipative time crystals are shown to be more robust against random noise in the drive, and are only weakly affected by the choice of initial state. We present the finite-size behaviour and the scaling of the lifetime of the time crystals with respect to the number of spins and the interactions strength, within a fully quantum mechanical description.