QS$G\hat{W}$：在$W$中包含梯形图的准粒子自洽$GW$方法
QS$G\hat{W}$: Quasiparticle Self consistent $GW$ with ladder diagrams in $W$
AI总结：
本研究提出纳入屏蔽库仑相互作用顶点修正的QS$G\hat{W}$方法，通过约40种半导体等多类体系测试，证实梯形图可显著改善QS$GW$的系统误差，并建立带隙与介电常数的关联以提升材料谱性质研究可靠性。
摘要：
我们提出了准粒子自洽$GW$近似（QS$GW$）[Phys. Rev. B, 76 165106 (2007)]的扩展版本，在屏蔽库仑相互作用$W$中纳入了顶点修正。该扩展通过求解布里渊区所有$k$点处极化矩阵的Bethe-Salpeter方程实现，我们将此方法命名为QS$G\hat{W}$。QS$GW$能对电子结构和光学响应给出合理且自洽的描述，但在多个性质上存在系统误差，尤其表现为倾向于高估绝缘体的带隙、使介电函数虚部中的等离激元峰蓝移，以及低估介电常数$\varepsilon_{\infty}$。本文的主要目标是评估在$W$中加入梯形图能在多大程度上改善QS$GW$近似针对绝缘体的系统误差。在基准测试中，我们选取了约40种研究较为充分的半导体，同时也考察了多种表征较少的非磁性体系、6种反铁磁氧化物以及亚铁磁体Fe$_3$O$_4$。我们发现，对于广泛的绝缘体体系，梯形图在单粒子格林函数和介电函数两方面都显著改善了QS$GW$的不足。研究中也出现了新的与实验不符的差异，本文的另一核心目标是明确这些误差的系统性程度，以及其是否可归因于理论中缺失的费曼图。本工作的一项关键发现是建立了带隙与介电常数$\varepsilon_{\infty}$之间的关联。同时良好描述这两个性质，能提供比单独描述任一性质更可靠的基准。我们展示了如何利用这一信息深化对SrTiO$_3$和FeO等材料体系中单粒子谱性质的理解。
英文摘要：
We present an extension of the quasiparticle self-consistent $GW$ approximation (QS$GW$) [Phys. Rev. B, 76 165106 (2007)] to include vertex corrections in the screened Coulomb interaction $W$. This is achieved by solving the Bethe-Salpeter equation for the polarization matrix at all $k$-points in the Brillouin zone. We refer to this method as QS$G\hat{W}$. QS$GW$ yields a reasonable and consistent description of the electronic structure and optical response, but systematic errors in several properties appear, notably a tendency to overestimate insulating bandgaps, blue-shift plasmon peaks in the imaginary part of the dielectric function, and underestimate the dielectric constant $ε_{\infty}$. A primary objective of this paper is to assess to what extent including ladder diagrams in $W$ ameliorates systematic errors for insulators in the QS$GW$ approximation. For benchmarking we consider about 40 well understood semiconductors, and also examine a variety of less well characterized nonmagnetic systems, six antiferromagnetic oxides, and the ferrimagnet Fe$_3$O$_4$. We find ladders ameliorate shortcomings in QS$GW$ to a remarkable degree in both the one-body Green's function and the dielectric function for a wide range of insulators. New discrepancies with experiment appear, and a key aim of this paper is to establish to what extent the errors are systematic and can be traced to diagrams missing from the theory. One key finding of this work is to establish a relation between the bandgap and the dielectric constant $ε_{\infty}$. Good description of both properties together provides a much more robust benchmark than either alone. We show how this information can be used to improve our understanding of the one-particle spectral properties in materials systems such as SrTiO$_3$ and FeO.
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