标题： DFT+U与DFT+DMFT的Hartree-Fock极限之间的等价性显式演示 显示英文标题

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

摘要： 几种方法已被开发出来，以改进强关联电子系统中密度泛函理论（DFT）的预测。 在这些方法中，DFT+$U$，对应于对局域相互作用的静态处理，以及将DFT与动力学平均场理论（DFT+DMFT）结合，考虑局域涨落，这两种方法在处理具有强局域电子-电子相互作用的材料描述方面都被证明非常有价值。 虽然原则上已知DFT+DMFT方法的Hartree-Fock（HF）极限应恢复DFT+$U$，但由于两种方法通常实现方式差异很大，因此在实践中证明这种等价性具有挑战性。 在本工作中，我们介绍了一种在Quantum ESPRESSO中使用Wannier90计算的Wannier函数进行DFT+$U$计算的方法，这使我们能够在DFT+$U$和DFT+DMFT中使用相同的Hubbard投影函数。 我们将这些DFT+$U$计算与DFT+DMFT计算进行基准测试，其中DMFT杂质问题是在HF近似下求解的。 考虑到包括NiO、MnO、LaMnO$_3$和LuNiO$_3$在内的多种典型材料，我们确立了两种方法的一致性。 最后，我们通过超越常用的原子轨道类投影器，展示了我们方法的通用性，通过对VO$_2$进行DFT+$U$计算，使用一组特殊的键中心Wannier函数。 显示英文摘要

摘要： 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.