Cavity quantum electrodynamics ring coupled cluster and the random phase approximation

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.