Entanglement growth in a weakly interacting Bose gas

The early stage of entanglement growth in a Bose system on a lattice is studied by means of analytical methods. A local unitary transformation is established which allows us to introduce Bose-Einstein condensation and the related weak-coupling approximation. We calculate both the entanglement of each lattice site with all other sites and the entanglement between pairs of sites. The first quantity weakly depends on the system size, while the second one exhibits peculiar oscillations within the time range of validity of our approximation.