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Few-Body Systems

Pairing correlations: I. The ground-state coupled-cluster formalism as a unifying approach

R. F. Bishop, Włodzimierz Piechocki, G. A. Stevens

Published Jan 1, 1988• 8 citations
Publisher
DOI
10.1007/bf01075347

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The coupled cluster [or exp(S)] formulation of quantum many-body theory is flrst extensively reviewed. It is then applied to the general problem of pairing correlations within a many-fermion system. The method is illustrated by restricting ourselves to the exact calculations that can be performed within the various generalized ladder approximations. It is shown how the formalism provides an efficient and unified framework in which to describe all aspects of pairing at the same level of approximation. Possible extensions to deal with composite clusters of more than two particles and to incorporate the effects of the collective excitations, are sketched
The ground-state pairing correlations in finite fermionic systems are described with a high degree of accuracy within a variational approach based on a combined coupled-cluster and particle-number-projected BCS ansatz. The flexibility of this symmetry-preserving wave function enables a unified picture valid from weak to strong coupling, both in small and large systems. The present variational approach consistently yields an energy upper bound while operating at the same level of precision as the nonvariational particle-number-projected Bogoliubov-coupled-cluster theory [Phys. Rev. C 99, 044301 (2019)].
In this paper, we develop a theoretical framework that extends single-reference (SR) coupled-cluster (CC) theory beyond its conventional role of describing a single electronic state-typically the lowest-energy state within the symmetry sector defined by the reference determinant. Rather than viewing the SR-CC cluster operator solely as a device for reproducing one target state, we consider more general constructions in which different components of the cluster operator play distinct roles, ranging from encoding states of different symmetry than the reference to enabling SR-CC Ansatz to describe multiple states simultaneously. These developments lead to a new class of SR-CC downfolding formalisms in which the resulting active-space effective Hamiltonians are capable of concurrently representing multiple correlated states nonorthogonal to the reference function. We establish three theorems that formalize this extension and demonstrate that standard CC downfolding emerges as a special case of the proposed framework. Finally, we introduce a Hermitian variant based on a unitary CC representation, which enables realistic simulations of ground and excited states while reducing the quantum resources required.