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arXiv:2512.14655

Testing electron-photon exchange-correlation functional performance for many-electron systems under weak and strong light-matter coupling

Iman Ahmadabadi, I-Te Lu, Leonardo A. Cunha, Michael Ruggenthaler, Johannes Flick, Angel Rubio

quant-phSubmitted Dec 16, 2025• Announced Dec 17, 2025
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Abstract

We present results of a photon-free exchange-correlation functional within the local density approximation (pxcLDA) for quantum electrodynamics density functional theory (QEDFT) that efficiently describes the electron density of many-electron systems across weak to strong light-matter coupling. Building on previous work [I-Te. Lu et al., Phys. Rev. A 109, 052823 (2024)] that captured electron-photon correlations via an exchange-correlation functional derived from the nonrelativistic Pauli-Fierz Hamiltonian and tested on one-electron systems, we use a simple procedure to compute a renormalization factor describing electron-photon correlations and inhomogeneity in the weak-coupling regime by comparing it with quantum electrodynamics coupled-cluster, and previous QEDFT optimized effective potential methods. Across various atoms and molecules, pxcLDA reproduces cavity-modified densities in close agreement with these references. The renormalization factor approaches unity as the system size or collective coupling increases, reflecting an electron-photon exchange-dominated behavior and improved accuracy for larger systems. This approach now offers a practical route to applying QEDFT functionals based on electron density to realistic electron systems.

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We present results of a photon-free exchange-correlation functional within the local density approximation (pxcLDA) for quantum electrodynamics density functional theory (QEDFT) that efficiently describes the electron density of many-electron systems across weak to strong light-matter coupling. Building on previous work [I-Te. Lu et al., Phys. Rev. A 109, 052823 (2024)] that captured electron-photon correlations via an exchange-correlation functional derived from the nonrelativistic Pauli-Fierz Hamiltonian and tested on one-electron systems, we use a simple procedure to compute a renormalization factor describing electron-photon correlations and inhomogeneity in the weak-coupling regime by comparing it with quantum electrodynamics coupled-cluster, and previous QEDFT optimized effective potential methods. Across various atoms and molecules, pxcLDA reproduces cavity-modified densities in close agreement with these references. The renormalization factor approaches unity as the system size or collective coupling increases, reflecting an electron-photon exchange-dominated behavior and improved accuracy for larger systems. This approach now offers a practical route to applying QEDFT functionals based on electron density to realistic electron systems.
Providing sufficient accuracy at low-computational cost, not surprisingly, density-functional theory ( DFT ) is a standard tool in theoretical material science. Similarly, quantum-electrodynamical density-functional theory ( QEDFT ) provides a promising route to describe experiments at the interface of quantum optics and quantum chemistry. Formally, in the Kohn-Sham ( KS ) formulation of DFT and QEDFT the exact many-particle Schrödinger equation is replaced by a set of coupled non-linear one-particle differential equations. The electron-electron, the electron-ion and the electron-photon interactions of the interacting system are mimicked by their corresponding effective KS potential with an, in principle unknown exchange-correlation ( xc ) term. In practice, DFT and QEDFT require approximations for this xc potential. The quality of which fully determines how much the DFT and QEDFT observables deviate from the exact ones. Understanding the shortcomings and improving the quality of approximate functionals makes the study of the exact functional of model systems indispensable. Here, we employ exact diagonalization for the Hamiltonian of different types of real-space lattice models in one spatial dimension to access the ground-state wave function, and thus to explicitly construct the exact functionals of DFT and QEDFT . To study the functional behavior of purely electronic systems, we consider two singlet-state electrons moving in an external potential with two connected atomic wells of variable depth and distance. To study coupled electron-photon systems, we consider the Rabi Hamiltonian with variable electron-photon coupling strength. By varying the model parameters, we systematically construct the functionals for systems from weak to strong coupling between the building blocks of the global system. Using the concept of the effective density-to- potential map, we discuss the intrasystem steepening which is an exact condition on the xc functional that captures the static correlation present in the system and carve out how it relates to the well-known intersystem derivative discontinuity. We further construct arbitrary observables as functionals of the internal variables which are directly affected by such features of the effective density-to-potential map. By constructing the reduced dipole map in the four-particle case of coupled electron-photon system, we show that the density-to-potential map helps to identify and understand recently discovered physical effects in the field of strongly coupled electron-photon systems. This work provides a contribution to the development of approximate function- als required in practical density-functional calculations of arbitrary experimentally accessible observables. Both the intrasystem steepening and the intersystem derivative discontinuity play a crucial role for systems with highly-localized electrons. Including both features in approximate functionals will improve the accu- racy of DFT evaluation of observables for such systems. Those results provide novel insight into the properties of the exact xc potentials in QEDFT . This work opens a new route to construct new functionals using coarse-grained or embed- ding approaches within the general and exact frameworks of DFT and QEDFT.
The last two decades have witnessed increasing experimental interest in the study and control of many-electron systems strongly interacting with quantum electromagnetic fields. This includes notable experiments in the areas of cavity and circuit quantum electrodynamics, quantum computing via photon mediated atom entanglement, electromagnetically induced transparency, quantum plasmonics, quantum simulators and chemistry. The description of realistic coupled matter-photon systems requires combining electronic structure methods from material science with quantum-optical methods. In this work, we propose a formally exact and numerically feasible approach, termed quantum electrodynamical time-dependent density functional theory (QED-TDDFT), that generalizes successful TDDFT for electronic structure calculations, to the electron-photon coupling. We develop a general framework for the description of coupled matter-photon systems in all possible realizations of interest, ranging from the fully relativistic case, to well-known quantum-optical model (e.g., the Rabi model). Of particular interest for condensed-matter applications is the density functionalisation of non-relativistic QED. The underlying theory in fact corresponds to standard non-relativistic quantum mechanics for the electrons, but with additional terms, which correct for relativity and electron-photon interactions. However, any application of density-functional theory requires approximations to the exchange-correlation (xc) functional. In this work we construct such an approximation for the description of electron-photon interaction effects in an optical cavity (the theory of reference is QED-TDDFT for many-electron systems coupled to cavity photons). The derived electron-photon optimized effective potential (OEP) reduces in the static limit to the Lamb shift of the ground state. The OEP is then tested on the Rabi model from weak to strong coupling regimes. The results are promising and open a path for describing complex strongly coupled matter-photon systems. Further, we consider the inclusion of relativistic spin-spin effects into the xc functional of standard spin density functional theory. In this way we provide quantum corrections that are essential for the description of magnetic inhomogeneities at the nanoscale. Such an approach improves over the current (classical) micromagnetic treatment of domain walls and skyrmions for spintronic applications.
Strong light-matter coupling enables hybrid states in which photonic and electronic degrees of freedom become correlated even in the ground state. While many-body effects in long-range dispersion interactions are known to reshape electronic properties under such conditions, their impact on quantum-optical observables remains largely unexplored. Here, we address this problem using quantum electrodynamical density-functional theory (QEDFT) combined with the recently developed photon-many-body dispersion (pMBD) functional, which can capture higher-order electron-photon correlations and multi-photon processes. We compute ground-state photonic observables including photon number fluctuations, second-order correlations, and quadrature variances, and find squeezing and super-Poissonian photon statistics emerging from light-matter interactions in the strong coupling regime. Our results demonstrate that capturing the full hierarchy of many-body, electron-photon and multi-photon correlations is essential for a consistent description of quantum-optical properties in strongly coupled molecular systems, establishing QEDFT as a first-principles framework for predicting nonclassical photonic features in the ground state of complex systems.
In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter-photon problems. We analyze model systems in optical cavities, where the matter-photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron-photon dynamics. This work paves the way to describe matter-photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science.
For certain correlated electron–photon systems we construct the exact density-to-potential maps, which are the basic ingredients of a density-functional reformulation of coupled matter-photon problems. We do so for numerically exactly solvable models consisting of up to four fermionic sites coupled to a single photon mode. We show that the recently introduced concept of the intra-system steepening (Dimitrov et al 2016 New J. Phys. 18 083004) can be generalized to coupled fermion-boson systems and that the intra-system steepening indicates strong exchange-correlation effects due to the coupling between electrons and photons. The reliability of the mean-field approximation to the electron–photon interaction is investigated and its failure in the strong coupling regime analyzed. We highlight how the intra-system steepening of the exact density-to-potential maps becomes apparent also in observables such as the photon number or the polarizability of the electronic subsystem. We finally show that a change in functional variables can make these observables behave more smoothly and exemplify that the density-to-potential maps can give us physical insights into the behavior of coupled electron–photon systems by identifying a very large polarizability due to ultra-strong electron–photon coupling.