Approaching a Floquet Time Crystal phase in the periodically driven O(N) model

Results are presented for the dynamics of the periodically driven O(N) model starting from a prescribed initial state. This model is known to host ferromagnetic phases that, depending on microscopic parameters, are period doubled or period synchronized, the former being an example of a Floquet Time Crystal. Employing numerical simulations, and analytic calculations within a large-N approach, we study how an initial paramagnetic phase evolves into the Floquet time crystal phase following a quench. We identify regimes where the transient dynamics is characterized by an effective mass that approaches steady state as a universal power-law. Results for the one-loop corrections to correlations functions in this transient regime are presented. Analogies to transient dynamics at the critical point of the static O(N) model are highlighted. The possibility of universality in the transition from the paramagnetic and Floquet time crystal phase is discussed.