Green’s Function Approach to the Bose-Hubbard Model


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 Greens 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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M. Ohliger and A. Pelster, "Green’s Function Approach to the Bose-Hubbard Model," World Journal of Condensed Matter Physics, Vol. 3 No. 2, 2013, pp. 125-130. doi: 10.4236/wjcmp.2013.32020.

Conflicts of Interest

The authors declare no conflicts of interest.


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