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

Proceedings Of The National Academy Of Sciences Of The United States Of America 118 (41), e2110464118 (2021)

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

Christian Schäfer, Florian Buchholz, Markus Penz, Michael Ruggenthaler, Angel Rubio

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.

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We thank G¨oran Johansson for helpful comments. This work was supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “CUI: Advanced Imaging of Matter” of the Deutsche Forschungsgemeinschaft (DFG) EXC 2056 (project ID 390715994), Grupos Consolidados (IT1249- 19), the Federal Ministry of Education and the Research Grant RouTe-13N14839, the SFB925 “Light induced dynamics and control of correlated quantum systems”, and the Swedish Research Council (VR) through Grant No. 2016-06059. M. P. acknowledges support by the Erwin Schr¨odinger Fellowship J 4107-N27 of the FWF (Austrian Science Fund)

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