Electron-photon exchange-correlation approximation for quantum-electrodynamical density-functional theory

I. Te Lu, Michael Ruggenthaler, Nicolas Tancogne-Dejean, Simone Latini, Markus Penz, Angel Rubio

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Abstract

Quantum-electrodynamical density-functional theory (QEDFT) provides a promising avenue for exploring complex light-matter interactions in optical cavities for real materials. Similar to conventional density-functional theory, the Kohn-Sham formulation of QEDFT needs approximations for the generally unknown exchange-correlation functional. In addition to the usual electron-electron exchange-correlation potential, an approximation for the electron-photon exchange-correlation potential is needed. A recent electron-photon exchange functional [C. Schäfer, Proc. Natl. Acad. Sci. USA 118, e2110464118 (2021)0027-842410.1073/pnas.2110464118], derived from the equation of motion of the nonrelativistic Pauli-Fierz Hamiltonian, shows robust performance in one-dimensional systems across weak- and strong-coupling regimes. Yet, its performance in reproducing electron densities in higher dimensions remains unexplored. Here we consider this QEDFT functional approximation from one- to three-dimensional finite systems and across weak to strong light-matter couplings. The electron-photon exchange approximation provides excellent results in the ultrastrong-coupling regime. However, to ensure accuracy also in the weak-coupling regime across higher dimensions, we introduce a computationally efficient renormalization factor for the electron-photon exchange functional, which accounts for part of the electron-photon correlation contribution. These findings extend the applicability of photon-exchange-based functionals to realistic cavity-matter systems, fostering the field of cavity QED (quantum-electrodynamics) materials engineering.

Original languageEnglish
Article number052823
JournalPhysical Review A
Volume109
Issue number5
Number of pages15
ISSN2469-9926
DOIs
Publication statusPublished - 2024

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