Quantum embedding methods for correlated excited states of point defects: Case studies and challenges

A quantitative description of the excited electronic states of point defects\nand impurities is crucial for understanding materials properties, and possible\napplications of defects in quantum technologies. This is a considerable\nchallenge for computational methods, since Kohn-Sham density-functional theory\n(DFT) is inherently a ground state theory, while higher-level methods are often\ntoo computationally expensive for defect systems. Recently, embedding\napproaches have been applied that treat defect states with many-body methods,\nwhile using DFT to describe the bulk host material. We implement such an\nembedding method, based on Wannierization of defect orbitals and the\nconstrained random-phase approximation approach, and perform systematic\ncharacterization of the method for three distinct systems with current\ntechnological relevance: a carbon dimer replacing a B and N pair in bulk\nhexagonal BN (C$_{\\text{B}}$C$_{\\text{N}}$), the negatively charged\nnitrogen-vacancy center in diamond (NV$^-$), and an Fe impurity on the Al site\nin wurtzite AlN ($\\text{Fe}_{\\text{Al}}$). For C$_{\\text{B}}$C$_{\\text{N}}$ we\nshow that the embedding approach gives many-body states in agreement with\nanalytical results on the Hubbard dimer model, which allows us to elucidate the\neffects of the DFT functional and double-counting correction. For the NV$^-$\ncenter, our method demonstrates good quantitative agreement with experiments\nfor the zero-phonon line of the triplet-triplet transition. Finally, we\nillustrate challenges associated with this method for determining the energies\nand orderings of the complex spin multiplets in $\\text{Fe}_{\\text{Al}}$.\n