Entanglement in one-dimensional bosonic chains

We studied the one-dimensional Bose-Hubbard model, by means of the Density Matrix Renormalization Group (DMRG). The U parameter, which contains the Coulombian repulsion information, is fixed to U = 1 and it is performed a swept over the hopping parameter t. The entanglement is investigated by implementing the one-site, two-site and block von Neumann entropy looking for which of these measures give account of the quantum phase transition from Mott insulator to superfluid. The one-site and two-site entropy do not give information of the phase transition of the system. In contrast, the block entropy shows, in the Mott insulator phase a behavior that saturates rapidly to a finite value and in the superfluid phase shows a logarithmic behavior that agrees with the mean field theory. From the derivative of the block entropy average as a function of t we found the phase transition takes place at t(c)=0.15.