  We study the superfluid-Mott insulator (SF-MI) transition in an
one-dimensional optical lattice system, and employ the Bose-Hubbard model in
two dimension with a combined potential of an optical lattice in one direction
and a confining harmonic trap in the other direction, which we refer to as the
pseudo one-dimension Bose-Hubbard model. There some excited states with respect
to the harmonic trap are considered. The Mott lobes shrink in the $\mu$ and $J$
directions of the $\mu$-$J$ 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 increases
because the energy spacing between the eigenstates of the Hamiltonian decreases
at finite temperature. The excited states significantly affect the robustness
of the MI phase at finite temperate.
