Explicit demonstration of the equivalence between DFT+U and the Hartree-Fock limit of DFT+DMFT

Several methods have been developed to improve the predictions of density functional theory (DFT) in the case of strongly correlated electron systems. Out of these approaches, DFT+U, which corresponds to a static treatment of the local interaction, and DFT combined with dynamical mean field theory (DFT+DMFT), which considers local fluctuations, have both proven incredibly valuable in tackling the description of materials with strong local electron-electron interactions. While it is in principle known that the Hartree-Fock (HF) limit of the DFT+DMFT approach should recover DFT+U, demonstrating this equivalence in practice is challenging, due to the very different ways in which the two approaches are generally implemented. In this work, we introduce a way to perform DFT+U calculations in QE using Wannier functions as calculated by Wannier90, which allows us to use the same Hubbard projector functions both in DFT+U and in DFT+DMFT. We benchmark these DFT+U calculations against DFT+DMFT calculations where the DMFT impurity problem is solved within the HF approximation. Considering a number of prototypical materials including NiO, MnO, LaMnO₃, and LuNiO₃, we establish the sameness of the two approaches. Finally, we showcase the versatility of our approach by going beyond the commonly used atomic orbital-like projectors by performing DFT+U calculations for VO₂ using a special set of bond-centered Wannier functions.