Quantum Electrodynamical time-dependent density functional theory
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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.