Quantum Monte Carlo assessment of embedding for for strongly correlated defects: interplay between mean-field starting point and interactions

Abstract

Point defects are of interest for many applications, from quantum sensing to modifying bulk properties of materials. Because of their localized orbitals, the electronic states are often strongly correlated, which has led to a proliferation of quantum embedding techniques to treat this correlation. In these techniques, most of the one-body states are treated with a weakly correlated theory such as density functional theory, and certain one-body states are singled out as an active space to be treated using an effective interaction. We assess these techniques for iron and chromium defects in aluminum nitride using quantum Monte Carlo (QMC) calculations on identical Hamiltonians. For these systems, we find the dominant errors in the embedding arise from the one-body crystal-field splitting in the d orbitals inherited from density functional theory (DFT), rather than double counting corrections, with the screened interactions also affected by the DFT orbitals. Strikingly, the best double counting recipe is opposite in these two cases. Because excitation energies can agree while the underlying wave functions do not, diagnosing these errors requires detailed information about the many-body wave functions, which QMC provides.