Kutepov A L
Ames Laboratory USDOE, Ames, IA 50011, USA.
J Phys Condens Matter. 2015 Aug 12;27(31):315603. doi: 10.1088/0953-8984/27/31/315603. Epub 2015 Jul 22.
Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ1 from the first-order perturbation theory, and the exact vertex Γ(E)). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. The results obtained with the exact vertex are directly related to the present open question-which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on perturbation theory (PT) systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.
已对两格点哈伯德模型（HM）的赫丁方程（HE）的自洽解进行了研究。已针对复杂度不断增加的三点顶点（Γ = 1（GW近似）、来自一阶微扰理论的Γ1以及精确顶点Γ(E)）找到这些解。在自洽迭代求解HE的过程中应用格林函数的额外准粒子（QP）近似的情况与未应用QP近似的情况之间进行了比较。用精确顶点获得的结果与当前的开放性问题直接相关——对于未来的实现，哪种近似更具优势，GW + DMFT还是QPGW + DMFT。结果表明，在强关联 regime 中，只有最初提出的GW + DMFT方案能够提供可靠的结果。当应用完全自洽时，基于微扰理论（PT）的顶点修正会系统地改进GW结果。应用QP自洽并结合PT顶点修正显示出与将精确顶点与QP自洽相结合的情况类似的问题。对本工作中研究的所有近似进行了沃德恒等式违反分析，并提供了其与所用方案的总体精度的关系。
