Photon-free QED functional in the weak light–matter coupling regime*

The intersection of quantum electrodynamics (QED) and density-functional theory (DFT) has opened up exciting opportunities in controlling quantum matter through light-matter coupling. This frontier, however, is beset with computational challenges, especially in the weak coupling regime. Building upon previous research, we present the results of nonperturbative photon-free QED functional in the long-wavelength limit, centered solely on the matter Hilbert space. This novel approach accurately reproduces QED's exact results in strong coupling, offering enhanced accuracy and computational efficiency. In this study, we present the results of this photon-free functional to facilitate QED-DFT calculations in the weak coupling regime, bridging the gap between quantum mechanics and quantum electrodynamics. We explore the energy and electronic density of polaritonic states using this approach, comparing our results with QED coupled cluster and optimized effective potential (OEP) calculations for a range of molecules and intermolecular interactions. Our findings shed light on the compatibility of this photon-free functional with practical applications, and provide a promising avenue for exploring quantum matter control in the presence of light-matter coupling.