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 veloctiy to other
characteristic velocities of the system, like the sound velocity. The
entanglement is investigated using two different measures, the von-Neuman
entropy and mutual information. Whereas the von-Neumann entropy grows rapidly
with time the mutual information between two small subsystems can as well
decrease after an initial increase. Additionally we show that the static von
Neuman entropy characterises the location of the quantum phase transition.Comment: 19 pages, 9 figure