Information propagation and equilibration in long-range Kitaev chains

We study the propagation of information through a Kitaev chain with long-range pairing interactions. Although the Lieb-Robinson bound is violated in the strict sense for long-range interacting systems, we illustrate that a major amount of information in this model still propagates ballistically on a light cone. We find a pronounced effect of the interaction range on the decay of the mutual information between spatially disconnected subsystems. A significant amount of information is shared at time-like separations. This regime is accompanied by very slow equilibration of local observables. As the Kitaev model is quasi-free, we illustrate how the distribution of quasi-particle group velocities explains the physics of this system qualitatively.