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
本研究以扩展哈伯德模型为基准，量化GW近似的误差，揭示顶点修正的相图依赖特性，发现静态COHSEX在特定U、V值下意外精确，为GW在关联材料中的应用提供了定量诊断。
AI 中文摘要
GW近似是材料中准粒子预测的标准工具，但其在关联系统中的适用范围仍缺乏量化，因为从头算顶点修正的计算成本极高。本研究以有限环上半填充扩展哈伯德模型的精确对角化结果作为数值精确参考，在相同希尔伯特空间中构建对应的模型空间GW理论，并量化其误差随局域（U）和非局域（V）相互作用强度的变化规律。研究发现顶点修正的性质在相图上存在转变：弱耦合区有效顶点Γ_eff < 1，反映精确短程关联对RPA电荷涨落的抑制；而在莫特区，Γ_eff单调增长（N=6时约为3，对应打开哈伯德能隙所需的局域顶点）。电子-空穴（极化率）通道的顶点修正会增大能隙误差，表明莫特能隙存在于自能通道。当V=0时，静态COHSEX在单一交叉点U*≈3.5t处意外精确；有限V通过非局域Fock交换将该点分裂为双交叉窗口，且该窗口向弱耦合区收缩。这些结果为GW在关联材料中的可靠性提供了定量诊断依据。
英文摘要
The $GW$ approximation is the standard tool for quasiparticle predictions in materials, yet its regime of validity in correlated systems remains poorly quantified, because \textit{ab initio} vertex corrections are computationally prohibitive. Using exact diagonalization of the half-filled extended Hubbard model on finite rings as a numerically exact reference, we construct the corresponding model-space $GW$ theory on the identical Hilbert space and quantify its error as a function of local ($U$) and non-local ($V$) interaction strength. We find that the required vertex correction changes character across the phase diagram: in the weak-coupling regime the effective vertex $Γ_{\rm eff} < 1$, reflecting the suppression of RPA charge fluctuations by exact short-range correlations, whereas in the Mott regime $Γ_{\rm eff}$ grows monotonically (to $\sim 3$ at $U=8t$ for $N=6$), reflecting the local dynamical self-energy structure required to open the Hubbard gap. Vertex corrections in the electron-hole (polarizability) channel are shown to \emph{worsen} the gap error, indicating that reproducing the Mott gap requires dynamical self-energy structure rather than improved screening. For $V=0$, static COHSEX is accidentally exact at a single crossover $U^* \approx 3.5\,t$; finite $V$, through non-local Fock exchange, splits this point into a double-crossover window that collapses toward weak coupling. Even at the crossover, however, the exact spectral function retains Hubbard-band structure that no static functional reproduces, so gap agreement does not imply functional accuracy. These results yield quantitative diagnostics for the reliability of $GW$ in correlated materials.
