Making ab initio QED functional(s): Non-perturbative and photon-free effective frameworks for strong light-matter coupling

TL;DR

This paper introduces a non-perturbative, photon-free formulation of quantum electrodynamics (QED) that simplifies the treatment of strong light-matter interactions in ab initio calculations, enabling practical applications to complex systems.

Contribution

It develops a matter-only, non-perturbative QED framework that accurately captures strong coupling effects and extends quantum-electrodynamical density-functional theory (QEDFT) with a simple, local-density-type functional.

Findings

Provides a photon-free QED formulation valid in various limits.

Constructs a new QEDFT functional accounting for quantized light.

Demonstrates applicability to periodic systems.

Abstract

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first-principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing, as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a non-perturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit, the infinite-frequency as well as the homogeneous limit and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows to extend the ansatz to the full minimal-coupling problem and to non-adiabatic situations. Finally, we provide a simple local-density-type functional that takes the strong coupling to the transverse photon-degrees of freedom into account and includes the correct frequency and polarization dependence. This is the first QEDFT functional that accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.