Out of Time Ordered Correlators (OTOCs) have been suggested as a probe of scrambling (generically referred as the delocalization of quantum information) and as a measure of chaos in quantum many-body systems. We explore scrambling in connection to entanglement dynamics in generic long-range systems, and in particular in the infinite-range Ising model. We study both bipartite and multipartite entanglement dynamics and we compare the results with the OTOCs of collective spin operators.

We argue that scrambling and entanglement growth are two distinct phenomena, characterized by two different time scales. While entanglements saturate at a time $t_{Ehr}\sim \sqrt N$ at which the semi-classical approximation breaks, the OTOCs keep growing in time up to $N$. Furthermore, by expanding in spin waves on top of the classical solution, we are able to device an approximated semi-analytic method that predicts the behavior of the OTOC up to $t_{Ehr}$. This method seems to be generic for long-range interacting hamiltonians and can be extended adding interaction to the hamiltonian.

* Silvia Pappalardi, SISSA, Trieste