发表机构
Technical University of Kenya（肯尼亚科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过精确数值基准检验等离激元极点近似，发现其在多尺度竞争材料中会误判带隙并掩盖准粒子失效，并提出基于谱权重多分散性的低成本诊断方法。
AI 中文摘要
$GW$ 近似是计算准粒子能带结构的黄金标准，但其计算成本常常迫使人们使用等离激元极点近似（PPA）。虽然已知 PPA 对简单金属和弱关联半导体具有高度准确性，但在具有竞争能量尺度的材料中，其有效性范围仍未得到充分量化。在此，我们利用有限一维 Hubbard 团簇上密度响应的 Lehmann 表示，构建了 PPA 的精确数值基准。通过将精确的非相互作用格林函数 $G_0$ 与屏蔽相互作用 $W$ 的精确极点表示解析卷积，我们无需数值频率积分即可计算 $GW$ 自能。我们证明，在单尺度 Mott 绝缘体中，矩守恒的 PPA 本质上是精确的。然而，在多带半导体中，带间跃迁引入了与高能 Mott 涨落竞争的低能屏蔽通道，PPA 会系统性地误判准粒子带隙达数个电子伏特。此外，我们表明强多极点屏蔽可以驱动精确准粒子权重 $Z \ o 0$，从而破坏准粒子图像——这一效应完全被 PPA 忽略，而 PPA 人为地稳定了尖锐的准粒子。最后，我们提出了一种基于损失函数谱权重的多分散性的计算廉价诊断方法，该方法能够从头开始准确预测 PPA 的失效。我们的结果为评估强关联材料中动态屏蔽近似的有效性提供了一个严格的框架。
英文摘要
The $GW$ approximation is the gold standard for calculating quasiparticle band structures, yet its computational cost frequently necessitates the use of the plasmon-pole approximation (PPA). While PPA is known to be highly accurate for simple metals and weakly correlated semiconductors, its regime of validity in materials with competing energy scales remains poorly quantified. Here, we construct an exact, numerical benchmark of the PPA using the Lehmann representation of the density response on finite one-dimensional Hubbard clusters. By analytically convolving the exact non-interacting Green's function $G_0$ with the exact pole representation of the screened interaction $W$, we compute the $GW$ self-energy without numerical frequency integration. We demonstrate that in single-scale Mott insulators, the moment-conserving PPA is essentially exact. However, in multi-band semiconductors where interband transitions introduce a low-energy screening channel that competes with high-energy Mott fluctuations, the PPA systematically misjudges the quasiparticle gap by several electron-volts. Furthermore, we show that strong multi-pole screening can drive the exact quasiparticle weight $Z \to 0$, destroying the quasiparticle picture-an effect entirely missed by the PPA, which artificially stabilizes sharp quasiparticles. Finally, we propose a computationally inexpensive diagnostic based on the polydispersity of the loss function's spectral weight, which accurately predicts PPA failure \textit{ab initio}. Our results provide a rigorous framework for assessing the validity of dynamical screening approximations in strongly correlated materials.
Comments6 pages, 4 figures, 2 tables
