Coupled-Cluster Theory for Systems of Bosons in External Traps

Abstract

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 $|{\varphi }_0>$. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of $|{\varphi }_0>$, the appearance of excitation operators $T={\sum }_{n=1}^N{T}_n$ 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 {\it depends} on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with $T=T_1+T_2$, i.e., coupled-cluster singles doubles (CCSD) are explicitly derived. Finally, an illustrative numerical example for a condensate with up to N=10000 bosons in an harmonic trap is provided and analyzed. The results are highly promising.

arXiv comment35 pages, 3 figures

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