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

Abstract

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 Quantum ESPRESSO 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, LaMnO${}_3$, and LuNiO${}_3$, 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 VO${}_2$ using a special set of bond-centered Wannier functions.

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Cited by in corpus (8)

• First-principles Hubbard parameters with automated and reproducible workflows
• Comparative analysis of methods for calculating Hubbard parameters using cRPA
• Comparative study of magnetic exchange parameters and magnon dispersions in NiO and MnO from first principles
• Impact of strong electronic correlations on altermagnets: the case of NiS2
• Pairing Symmetry Crossover from $d$-wave to $s_{\pm }$-wave in a Bilayer Nickelate Driven by Hund's Coupling and Crystal Field Splitting
• Electronic correlations and spin-charge-density stripes in double-layer La${}_3$Ni${}_2$O${}_7$
• Getting the manifold right: The crucial role of orbital resolution in DFT+U for mixed d-f electron compounds
• Bridging constrained random-phase approximation and linear response theory for computing Hubbard parameters