Effects of finite temperature on the robustness of the Mott insulator   phase in pseudo one-dimensional Bose-Hubbard Model
  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. 
Motoyoshi Inoue, Keita Kobayashi, Yusuke Nakamura, and Yoshiya   Yamanaka
cond-mat.quant-gas