Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory

TL;DR

This paper formally connects particle-particle RPA with coupled cluster doubles, revealing their relationship through a quasiparticle formalism and highlighting the importance of mosaic terms for accurate fermionic descriptions.

Contribution

It establishes a formal link between pp-RPA and ladder-CCD within a quasiparticle RPA framework, introducing the concept of crossed-ring and mosaic terms for improved fermionic modeling.

Findings

Connected pp-RPA and ladder-CCD via quasiparticle formalism.

Highlighted the role of mosaic terms in fermionic antisymmetry.

Suggested potential for improved RPA-based density functionals.

Abstract

We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a correct bosonization in the sense that the wavefunction and Hilbert space are exactly fermionic. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call "crossed-ring" whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call "mosaic" terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA an d qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.