Light-cone velocities after a global quench in a non-interacting model

We study the light-cone velocity for global quenches in the non-interacting XY chain starting from a class of initial states that are eigenstates of the local $z$-component of the spin. We point out how translation invariance of the initial state can affect the maximal speed at which correlations spread. As a consequence the light-cone velocity can be state-dependent also for non-interacting systems: a new effect of which we provide clear numerical evidence and analytic predictions. Analogous considerations, based on numerical results, are drawn for the evolution of the entanglement entropy.