Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model

We investigate the spreading of information in a one-dimensional Bose–Hubbard system after a sudden parameter change. In particular, we study the time evolution of correlations and entanglement following a quench. The investigated quantities show a light-cone-like evolution, i.e. the spreading with a finite velocity. We discuss the relation of this velocity to other characteristic velocities of the system, like the sound velocity. The entanglement is investigated using two different measures, the von Neumann entropy and mutual information. Whereas the von Neumann entropy grows rapidly with time the mutual information between two small subsystems can decrease as well after an initial increase. Additionally we show that the static von Neumann entropy characterizes the location of the quantum phase transition