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 and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (CBCN), the negatively charged nitrogen-vacancy center in diamond (NV-), and an Fe impurity on the Al site in wurtzite AlN (FeAl). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the "double-counting"correction. For CBCN we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the NV- center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in FeAl.