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M. P. A. Fisher, P. B. Weichman, G. Grinstein and D. S. Fisher, “Boson Localization and the Superfluid-Insulator Transition,” Physical Review B, Vol. 40, No. 1, 1989, pp. 546-570. doi:10.1103/PhysRevB.40.546

has been cited by the following article:

• TITLE: Green’s Function Approach to the Bose-Hubbard Model

  AUTHORS: Matthias Ohliger, Axel Pelster

  KEYWORDS: Bose-Hubbard Model; Quantum Phase Transition; Phase Boundary

  JOURNAL NAME: World Journal of Condensed Matter Physics, Vol.3 No.2, May 24, 2013

  ABSTRACT: We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green’s function approach allows for calculating the excitation spectrum both for zero and finite temperature and for determining the effective masses of particles and holes.