Cavity Quantum Electrodynamics Ring Coupled Cluster and the Random Phase Approximation

TL;DR

This work proves a formal and numerical equivalence between cavity QED-RPA and QED ring-CCD for ground-state correlation energy. It starts from the Pauli-Fierz Hamiltonian, constructs a QED-HF reference, and develops QED-RPA and ring-CCD with explicit electron-photon couplings. It uses a Riccati reformulation to show $E_c^{dRPA}=E_c^{drCCD}$ and validates the result on a water molecule in a single-mode cavity, finding near-perfect agreement across couplings. The findings highlight the significance of photon channels, such as double photon creation, and position QED-RPA as an efficient tool for large-scale predictions of cavity-modified properties.

Abstract

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 [{\em J. Chem. Phys.} {\bf 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.