多极近似下 $GW$ 自能高效解析表示所给出的谱性质
Spectral properties from an efficient analytical representation of the $GW$ self-energy within a multipole approximation
AI总结：
本文提出 $GW$ 自能的多极解析表示 MPA-$\Sigma$，并结合 MPA-$W$ 与 MPA-$G$ 高效计算谱性质，在多类材料和分子中验证其精度。
摘要：
我们通过多极近似（MPA-$\Sigma$）提出了频率依赖的 $GW$ 自能 $\Sigma$ 的高效解析表示。自能的 multipole-Padé 模型由复频率平面中少量 $\Sigma$ 的数值计算结果插值得到，这类似于此前为屏蔽库仑相互作用发展的多极表示（MPA-$W$）[Phys. Rev. B \textbf{104}, 115157 (2021)]。我们表明，与 MPA-$W$ 一样，MPA-$\Sigma$ 中频率采样的适当选择对于保证计算效率和高精度至关重要。MPA-$W$ 与 MPA-$\Sigma$ 的组合方案显著降低了全频率自能计算的成本，尤其是宽能量范围内的谱能带结构计算。关键在于，MPA-$\Sigma$ 使相互作用格林函数 $G$ 的多极表示（MPA-$G$）成为可能，从而可直接计算所有谱性质，并提供一种定义重整化因子 $Z$ 的更一般方法。我们在多种体系上验证了 MPA-$\Sigma$ 和 MPA-$G$ 方法：体相 Si、Na 和 Cu、单层 MoS$_2$、NaCl 离子对以及 F$_2$ 分子。此外，我们引入 toy MPA-$\Sigma$/$G$ 模型，以考察弱关联和强关联不同区间中的准粒子图像。利用这些模型，我们揭示了由 $\Sigma$ 的局域导数定义 $Z$ 所存在的局限。
英文摘要：
We propose an efficient analytical representation of the frequency-dependent $GW$ self-energy $Σ$ via a multipole approximation (MPA-$Σ$). The multipole-Padé model for the self-energy is interpolated from a small set of numerical evaluations of $Σ$ in the complex frequency plane, similarly to the previously multipole representation developed for the screened Coulomb interaction (MPA-$W$) [Phys. Rev. B \textbf{104}, 115157 (2021)]. We show that, likewise MPA-$W$, an appropriate choice of frequency sampling in MPA-$Σ$ is critical to guarantee computational efficiency and high accuracy. The combined MPA-$W$ and MPA-$Σ$ scheme considerably reduces the cost of full-frequency self-energy calculations, especially for spectral band structures over a wide energy range. Crucially, MPA-$Σ$ enables a multipole representation for the interacting Green's function $G$ (MPA-$G$), providing a straightforward evaluation of all the spectral properties, and a more general way to define the renormalization factor $Z$. We validate the MPA-$Σ$ and MPA-$G$ approaches for diverse systems: bulk Si, Na and Cu, monolayer MoS$_2$, the NaCl ion-pair and the F$_2$ molecule. Moreover, we introduce toy MPA-$Σ$/$G$ models to examine the quasiparticle picture in different regimens of weak and strong correlation. With these models, we expose limitations in defining $Z$ from the local derivative of $Σ$.
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