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A strong-coupling expansion for the Green's functions, self-energies andcorrelation functions of the Bose Hubbard model is developed. We illustrate thegeneral formalism, which includes all possible inhomogeneous effects in theformalism, such as disorder, or a trap potential, as well as effects of thermalexcitations. The expansion is then employed to calculate the momentumdistribution of the bosons in the Mott phase for an infinite homogeneousperiodic system at zero temperature through third-order in the hopping. Byusing scaling theory for the critical behavior at zero momentum and at thecritical value of the hopping for the Mott insulator to superfluid transitionalong with a generalization of the RPA-like form for the momentum distribution,we are able to extrapolate the series to infinite order and produce veryaccurate quantitative results for the momentum distribution in a simplefunctional form for one, two, and three dimensions; the accuracy is better inhigher dimensions and is on the order of a few percent relative erroreverywhere except close to the critical value of the hopping divided by theon-site repulsion. In addition, we find simple phenomenological expressions forthe Mott phase lobes in two and three dimensions which are much more accuratethan the truncated strong-coupling expansions and any other analyticapproximation we are aware of. The strong-coupling expansions and scalingtheory results are benchmarked against numerically exact QMC simulations in twoand three dimensions and against DMRG calculations in one dimension. Theseanalytic expressions will be useful for quick comparison of experimentalresults to theory and in many cases can bypass the need for expensive numericalsimulations.

Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results