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

TL;DR

This paper demonstrates the theoretical and practical equivalence between DFT+U and the Hartree-Fock limit of DFT+DMFT by implementing a unified approach using Wannier functions, validated on several correlated materials.

Contribution

The authors introduce a method to perform DFT+U calculations with Wannier functions in Quantum ESPRESSO, enabling direct comparison with DFT+DMFT and establishing their equivalence in the Hartree-Fock limit.

Findings

DFT+U and DFT+DMFT are equivalent in the Hartree-Fock limit.

Benchmarking on NiO, MnO, LaMnO3, and LuNiO3 confirms the sameness of the approaches.

Versatility demonstrated with bond-centered Wannier functions for VO2.

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.