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Green's function formulation of quantum defect embedding theory

We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the $G_0 W_0$ approximation. We then show the robustness of our methodology by applying the theory with the newly derived scheme to several defects in diamond. Additionally, we discuss a strategy to obtain converged results as a function of the size and composition of the active space. Our results show that QDET is a promising approach to investigate strongly correlated states of defects in solids.