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 wavefunction is obtained by applying an exponential operator exp{T} to the ground configuration |φ0〉. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of |φ0〉, the appearance of excitation operators T = ∑N n=1 Tn for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupledcluster 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 (CCSD) are explicitly derived. Finally, an illustrative numerical ex∗E-mail: [email protected] †E-mail: [email protected] ‡E-mail: [email protected] 1 ample for a condensate with up to N = 10000 bosons in an harmonic trap is provided and analyzed. The results are highly promising. PACS numbers: 03.75.Hh, 03.65.-w Typeset using REVTEX 2