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Recent experimental advances in strongly coupled light-matter systems hassparked the development of general ab-initio methods capable of describinginteracting light-matter systems from first principles. One of these methods,quantum-electrodynamical density-functional theory (QEDFT), promisescomputationally efficient calculations for large correlated light-mattersystems with the quality of the calculation depending on the underlyingapproximation for the exchange-correlation functional. So far no truedensity-functional approximation has been introduced limiting the efficientapplication of the theory. In this paper, we introduce the first gradient-baseddensity functional for the QEDFT exchange-correlation energy derived from theadiabatic-connection fluctuation-dissipation theorem. We benchmark thissimple-to-implement approximation on small systems in optical cavities anddemonstrate its relatively low computational costs for fullerene molecules upto C$_{180}$ coupled to 400,000 photon modes in a dissipative optical cavity.This work now makes first principle calculations of much larger systemspossible within the QEDFT framework effectively combining quantum optics withlarge-scale electronic structure theory.

Simple Exchange-Correlation Energy Functionals for Strongly Coupled Light-Matter Systems based on the Fluctuation-Dissipation Theorem