Cold bosons in optical lattices: an exact diagonalization study

Abstract

Experimental setups of cold atoms in optical lattices reproduce several quantum many-particle models, including the Bose-Hubbard model. We study this model by means of exact diagonalization. This model carries a super uid to Mott insulator quantum phase transition. In order to characterize the phase transition, we have computed the ground state of the system and its overlap with the analytic expressions for the Mott insulator and super uid states, its one-body density matrix, and its Von Neumann entropy. We have also studied the e ect of setting an attractive bias potential in one site of the lattice at di erent strengths and also the strongly biased case in the repulsive regime. Finally, we have also explored the case with attractive on-site interactions, nding correlated states in the weakly attractive regime.