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

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Lu,  I-T.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science;

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Ruggenthaler,  M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science;

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Tancogne-Dejean,  N.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science;

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Latini,  S.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science;
Department of Physics, Technical University of Denmark;

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Penz,  M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science;
Department of Computer Science, Oslo Metropolitan University;

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Rubio,  A.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science;
Center for Computational Quantum Physics (CCQ), The Flatiron Institute;

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PhysRevA.109.052823.pdf
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Citation

Lu, I.-T., Ruggenthaler, M., Tancogne-Dejean, N., Latini, S., Penz, M., & Rubio, A. (2024). Electron-photon exchange-correlation approximation for quantum-electrodynamical density-functional theory. Physical Review A, 109(5): 052823. doi:10.1103/PhysRevA.109.052823.


Cite as: https://hdl.handle.net/21.11116/0000-000E-6E7C-D
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 et al., Proc. Natl. Acad. Sci. USA 118, e2110464118 (2021)], 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.