GW and Bethe-Salpeter Theory for Molecular Polaritons, Quasiparticles, and Excitons
Abstract
The electron self-energy is central to quasiparticle theory, yet how an optical cavity enters it remains unclear. We address this question for a molecule in a single-mode cavity using the dipole-gauge Pauli-Fierz Hamiltonian and a coherent-state QED Hartree-Fock reference. The cavity enters through three channels: the static dipole self-energy (DSE) shift of reference orbital energies, direct DSE augmentation of the screened interaction, and the polariton pole carrying the bilinear electron-photon coupling. We benchmark QED-GW ionization potentials (IPs) and electron affinities (EAs) against a cavity Δ-method ladder from QED-HF to correlated wave-function methods, whose cavity-induced shifts agree within 1 meV where directly comparable. For closed-shell molecules with unbound anions, GW systematically overestimates cavity-induced IP redshifts, whereas EA shifts are reproduced nearly quantitatively, although this does not imply comparable accuracy for absolute EAs. For ionic molecules with bound anions, this ordering reverses, consistent with published QED coupled-cluster results. Coupling and detuning scans show that the error is predominantly quadratic in λ and DSE-driven rather than resonant. The spectral function develops a polariton-replica photoemission sideband with weight scaling as λ2. In the static screened interaction used in the Bethe-Salpeter equation, bare-photon exchange cancels the matching DSE contribution to the direct interaction, while exchange and polariton-screening corrections remain. Their net effect on the lowest excitation is appreciable only for ammonia in the molecules studied. Exciton-binding energies involving unbound anions are strongly basis-dependent and should therefore be viewed as diagnostics of electron-hole interactions rather than basis-converged molecular quantities.
Related
- Nonuniform Screening Reshapes Collective Excitons in Molecular Aggregates from Stochastic Bethe-Salpeter Theory
- Vibrational Dressing of Collective Molecular Polaritons: A Scalable Green's-Function Theory
- Disorder-Induced Eigenstate Localization of Molecular Polaritons Despite Spectroscopic Strong Coupling
- Non-equilibrium cavity pumping of electronic molecular polaritons
- Real-Time Approach to the Dynamical Bethe-Salpeter Equation for Finite Systems
BibTeX
@misc{willow2026bethesalpeter,
title = {{GW and Bethe-Salpeter Theory for Molecular Polaritons, Quasiparticles, and Excitons}},
author = {Soohaeng Yoo Willow and Gi Beom Sim and Tae Hyeon Park and Tae In Kim and D. ChangMo Yang and Mikuláš Matoušek and Jiří Brabec and Libor Veis and Chang Woo Myung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00594},
eprint = {2609.00594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00594},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GW and Bethe-Salpeter Theory for Molecular Polaritons, Quasiparticles, and Excitons
AU - Soohaeng Yoo Willow
AU - Gi Beom Sim
AU - Tae Hyeon Park
AU - Tae In Kim
AU - D. ChangMo Yang
AU - Mikuláš Matoušek
AU - Jiří Brabec
AU - Libor Veis
AU - Chang Woo Myung
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.00594
UR - https://arxiv.org/abs/2609.00594
AB - The electron self-energy is central to quasiparticle theory, yet how an optical cavity enters it remains unclear. We address this question for a molecule in a single-mode cavity using the dipole-gauge Pauli-Fierz Hamiltonian and a coherent-state QED Hartree-Fock reference. The cavity enters through three channels: the static dipole self-energy (DSE) shift of reference orbital energies, direct DSE augmentation of the screened interaction, and the polariton pole carrying the bilinear electron-photon coupling. We benchmark QED-GW ionization potentials (IPs) and electron affinities (EAs) against a cavity Δ-method ladder from QED-HF to correlated wave-function methods, whose cavity-induced shifts agree within 1 meV where directly comparable. For closed-shell molecules with unbound anions, GW systematically overestimates cavity-induced IP redshifts, whereas EA shifts are reproduced nearly quantitatively, although this does not imply comparable accuracy for absolute EAs. For ionic molecules with bound anions, this ordering reverses, consistent with published QED coupled-cluster results. Coupling and detuning scans show that the error is predominantly quadratic in λ and DSE-driven rather than resonant. The spectral function develops a polariton-replica photoemission sideband with weight scaling as λ^2. In the static screened interaction used in the Bethe-Salpeter equation, bare-photon exchange cancels the matching DSE contribution to the direct interaction, while exchange and polariton-screening corrections remain. Their net effect on the lowest excitation is appreciable only for ammonia in the molecules studied. Exciton-binding energies involving unbound anions are strongly basis-dependent and should therefore be viewed as diagnostics of electron-hole interactions rather than basis-converged molecular quantities.
ER -