Quantum phase transitions in optical lattices beyond the Bogoliubov approximation

We study quantum phase transition from the superfluid to a Mott insulator in optical lattices using a Bose-Hubbard Hamiltonian. For this purpose we have developed a field theoretical approach in terms of path integral formalism to calculate the second-order quantum corrections to the energy density as well as to the superfluid fraction in cubic optical lattices. Using present approach the condensate fraction and ground state energy are calculated as functions of the s-wave scattering length. In contrast to the Bogoliubov model, which is technically speaking a one-loop approximation, we carry the calculation up to two loops, and improve the result further by variational perturbation theory. The result suggests that the quantum phase transition exists