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

Abstract

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 (${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$), the negatively charged nitrogen-vacancy center in diamond (${\mathrm{NV}}^{\ensuremath{-}}$), and an Fe impurity on the Al site in wurtzite AlN (${\text{Fe}}_{\text{Al}}$). 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 ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$ 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 ${\mathrm{NV}}^{\ensuremath{-}}$ 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 ${\text{Fe}}_{\text{Al}}$.