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

Recent experimental advances in strongly coupled light-matter systems have sparked the development of general ab initio methods capable of describing interacting light-matter systems from first principles. One of these methods, quantum-electrodynamical density-functional theory (QEDFT), promises computationally efficient calculations for large correlated light-matter systems with the quality of the calculation depending on the underlying approximation for the exchange-correlation functional. So far no true density-functional approximation has been introduced limiting the efficient application of the theory. In this Letter, we introduce the first gradient-based density functional for the QEDFT exchange-correlation energy derived from the adiabatic-connection fluctuation-dissipation theorem. We benchmark this simple-to-implement approximation on small systems in optical cavities and demonstrate its relatively low computational costs for fullerene molecules up to ${\mathrm{C}}_{180}$ coupled to 400 000 photon modes in a dissipative optical cavity. This Letter now makes first principle calculations of much larger systems possible within the QEDFT framework effectively combining quantum optics with large-scale electronic structure theory.

Figure 1

Comparison of the different schemes for the beryllium atom and the LiH molecule. In (a) we show the absolute energy scale of the beryllium atom for the KLI (black), OEP (blue), GA (red), and OEP-ss (single shot) (green). (b) The difference in percentage of KLI (black), GA (red), and OEP-ss (single shot) (green) with respect to the OEP energies. Same for the LiH molecule in (c) and (d), respectively.

Figure 2

Spectral densities and electron-photon energy for $C_{20}$, $C_{60}$, and $C_{180}$. In (a), we show the spectral density with different ${\lambda }_{\alpha }$ values over cavity frequency ${\omega }_{\alpha }$ for $\kappa =0.01\mathrm{eV}$ in black, $\kappa =0.1\mathrm{eV}$ in blue, and $\kappa =1\mathrm{eV}$ in red. (b) The electron-photon energy $E_{\mathrm{XC}}^{(\mathrm{GA})}/N_{\text{at}}$ for ${\mathrm{C}}_{20}$ (blue), ${\mathrm{C}}_{60}$ (black), and $C_{180}$ (red) for different dissipation constants $\kappa \in [0,1]\mathrm{eV}$.