It is well known that the ground-state correlation energy from the particle-hole channel of the random phase approximation (RPA) is formally equivalent to that from a simplified coupled cluster doubles (CCD) model that includes only ring-diagram contraction contributions in the residual equations Scuseria et al., J. Chem. Phys. 129, 231101 (2008). We generalize this analytic result to the cavity quantum electrodynamics (QED) case and demonstrate the numerical equivalence of QED-RPA and a QED ring-CCD model that accounts for double electron excitations, coupled single-electron excitations/single-photon creation, and double-photon creation.
DePrince et al. (Tue,) studied this question.