局域势泛函嵌入理论：一种自洽的密度泛函理论
Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals
摘要：
最近提出的Householder变换密度矩阵功能嵌入理论（Ht-DMFET）[Sekaran等人，Phys. Rev. B 104，035121（2021）]，其等价于（但形式上比）非相互作用情况下的密度矩阵嵌入理论（DMET），从密度泛函理论（DFT）的角度重新审视。本文推导了一种适用于含单一杂质的一维Hubbard晶格的密度泛函型HT-DMFET。在已有的密度泛函近似的基础上，提出并实现了局域势泛函嵌入理论。尽管LPFET在低密度区的表现优于Ht-DMFET，特别是当电子相关性较强时，但这两种方法都无法描述密度驱动的Mott-Hubbard跃迁。这些结果结合我们的正式精确的密度泛函嵌入理论表明，一个单一的静态嵌入杂质可以在原则上描述的间隙开口，提供的互补相关势（描述的嵌入集群与其环境的相互作用，这是简单地忽略在HT-DMFET和LPFET）表现出导数不连续（DD）在半填充。将LPFET扩展到多个杂质（这将使得能够规避DDs的建模）及其推广到量子化学哈密顿量的工作留给未来的工作。
英文摘要：
The recently proposed Householder transformed density-matrix functional embedding theory (Ht-DMFET) [Sekaran et al., Phys. Rev. B 104, 035121 (2021)], which is equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, is revisited from the perspective of density-functional theory (DFT). An in-principle-exact density-functional version of Ht-DMFET is derived for the one-dimensional Hubbard lattice with a single embedded impurity. On the basis of well-identified density-functional approximations, a local potential functional embedding theory (LPFET) is formulated and implemented. Even though LPFET performs better than Ht-DMFET in the low-density regime, in particular when electron correlation is strong, both methods are unable to describe the density-driven Mott-Hubbard transition, as expected. These results combined with our formally exact density-functional embedding theory reveal that a single statically embedded impurity can in principle describe the gap opening, provided that the complementary correlation potential (that describes the interaction of the embedding cluster with its environment, which is simply neglected in both Ht-DMFET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work.
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