Double-counting and hybridization in quantum defect embedding theory

Quantum Defect Embedding theory (QDET) [1-3] is a many-body embedding method designed to describe solids with strongly correlated electrons localized within a given region of space, such as spin defects in semiconductors and insulators. Previous formulations of QDET have been successful in predicting the electronic properties of several point-defects, including the nitrogen-vacancy center in diamond, but encountered limitations in other cases. In this work, we discuss several important aspects previously underexplored in Ref. [2], including a re-derivation of double-counting corrections (DCC) for frequency independent electronic screening and the inclusion of host-defect hybridization, which may be significant in systems with strong bulk-defect interactions. We illustrate the effect of DCC and hybridization on the multi-reference states of the neutral silicon-vacancy in diamond and the negatively charged boron-vacancy in h-BN, showing an improvement of our results, compared to experiments, over our previous approach [2]. We also discuss further developments of QDET, including self-consistency and frequency-dependent screening. Our approach strengthens the accuracy of QDET for spin-defects in solids and extends the scope of the theory to more challenging materials and applications.