Testing electron-photon exchange-correlation functional performance for many-electron systems under weak and strong light-matter coupling.

We present results for a photon-free exchange-correlation functional within the local density approximation (pxcLDA) for quantum electrodynamics density functional theory (QEDFT), which efficiently describes the electron density of many-electron systems across weak to strong light-matter coupling. Building on previous work [Lu et al., Phys. Rev. A 109, 052823 (2024)] that captured electron-photon correlations via an exchange-correlation functional derived from the nonrelativistic Pauli-Fierz Hamiltonian and tested on one-electron systems, we use a simple procedure to compute a renormalization factor describing electron-photon correlations and inhomogeneity in the weak-coupling regime by comparing it with quantum electrodynamics coupled-cluster and previous QEDFT optimized effective potential methods. Across various atoms and molecules, pxcLDA reproduces cavity-modified densities in close agreement with these references. The renormalization factor approaches unity as the system size or collective coupling increases, reflecting an electron-photon exchange-dominated behavior and improved accuracy for larger systems. This approach now offers a practical route to applying QEDFT functionals based on electron density to realistic electron systems.