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.