Coupled-cluster theory for systems of bosons in external traps

A coupled-cluster approach for systems of N bosons in external traps is developed. In the coupled-cluster approach the exact many-body wave function is obtained by applying an exponential operator exp{T} to the ground configuration 0. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of 0, the appearance of excitation operators T = n=1 N Tn for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupled-cluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupled-cluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupled-cluster expansions are size consistent, for bosons the answer to this question depends on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with T= T1 + T2, i.e., coupled-cluster singles doubles are explicitly derived. Finally, an illustrative numerical example for a condensate with up to N=10 000 bosons in an harmonic trap is provided and analyzed. The results are highly promising.