Green's Function Approach to the Bose-Hubbard Model
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.
Cite
@article{arxiv.0810.4399,
title = {Green's Function Approach to the Bose-Hubbard Model},
author = {Matthias Ohliger and Axel Pelster},
journal= {arXiv preprint arXiv:0810.4399},
year = {2013}
}