Scrambling and entanglement spreading in long-range spin chains

We study scrambling in connection to multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are found to be very different: up to the Ehrenfest time they rise side by side departing only afterwards. Entanglement saturates and becomes extensively multipartite, while scrambling continues its growth up to the recurrence time. Remarkably, the exponential behaviour of scrambling emerges not only in the chaotic case, but also in the regular one, when the dynamics occurs at a dynamical critical point.