Green's Function Approach to the Bose-Hubbard Model

Matthias Ohliger; Axel Pelster

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arXiv · 0810.4399

Green's Function Approach to the Bose-Hubbard Model

Matthias Ohliger·Axel Pelster

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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 the latest high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green's function approach allows for calculating the excitation spectrum at finite temperature and for determining the effective masses of particles and holes.

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Matthias Ohliger, Axel Pelster. 2013-05-29. Green's Function Approach to the Bose-Hubbard Model. https://arxiv.org/abs/0810.4399

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