Coupled-Cluster Theory for Systems of Bosons in External Traps

TL;DR

This paper develops a coupled-cluster method for large bosonic systems in traps, addressing size consistency issues and deriving explicit equations for CCSD, with promising numerical results for condensates of up to 10,000 bosons.

Contribution

It introduces a coupled-cluster approach tailored for bosonic systems, including size consistency analysis and explicit CCSD equations, enabling treatment of large condensates.

Findings

Coupled-cluster approach effectively models large bosonic systems.

Size consistency depends on the choice of ground configuration for bosons.

Numerical example shows promising results for condensates of up to 10,000 bosons.

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 $|\phi_0>$. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of $|\phi_0>$, 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.