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Green’s Function Approach to the Bose-Hubbard Model

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Author(s): Matthias Ohliger | Axel Pelster

Journal: World Journal of Condensed Matter Physics
ISSN 2160-6919

Volume: 03;
Issue: 02;
Start page: 125;
Date: 2013;
Original page

Keywords: Bose-Hubbard Model | Quantum Phase Transition | Phase Boundary

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.
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