Effects of finite temperature on the robustness of the Mott insulator phase in a pseudo-two-dimensional Bose-Hubbard model

We study the superfluid-Mott insulator (SF-MI) transition in a two-dimensional optical lattice system and employ the Bose-Hubbard model in three dimensions with a combined potential of an optical lattice in two directions and a confining harmonic trap in the other direction, which we refer to as the pseudo-two-dimensional Bose-Hubbard model. Some excited states with respect to the harmonic trap are taken into account in this paper. The Mott lobes shrink in the μ and J directions of the μ-J phase diagram. The shrinkage occurs because the interactions involving the excited states become weaker than that between particles in the ground state. The dispersion of the in-site particle number increases because the energy spacing between the eigenstates of the Hamiltonian decreases at finite temperature. The presence of the excited states significantly affects the robustness of the MI phase at finite temperature.