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

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.