Entanglement in the Bogoliubov vacuum

We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second-order approximation to the ground state of an interacting Bose-Einstein condensate. We work on one- and two-dimensional lattices and study the entanglement between two groups of lattice sites as a function of the geometry of the configuration and the strength of the interactions. As our measure of entanglement we use the logarithmic negativity, supplemented by an algorithmic check [G. Giedke et al., Phys. Rev. Lett. 87, 167904 (2001)] for bound entanglement where appropriate. The short-range entanglement is found to grow approximately linearly with the group sizes and to be favored by strong interactions. Conversely, long-range entanglement is favored by relatively weak interactions. No examples of bound entanglement are found.