Dynamical Mean Field Theory for the Bose-Hubbard Model
arXiv:0907.2928 · doi:10.1103/PhysRevB.80.245110
Abstract
The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the plane and on the plane are produced ( is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.
11 pages, 8 figures
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