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 BoseHubbard system after a sudden parameter change. In particular, we study the timeevolution 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 sub-systems 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. PACS numbers: 03.75.Lm 05.70.Ln 67.40.Fd73.43.Nq ar X iv :0 80 3. 29 47 v2 [ co nd -m at .o th er ] 3 J un 2 00 8 Correlations and entanglement after a quench in the Bose-Hubbard model 2