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
本研究通过精确对角化最小Hubbard簇，证明在阻挫簇上GW和GW+DMFT均违反Matsubara因果性，局域自能修正不足以保证因果解析结构，需非局域顶点修正。
AI 中文摘要
$GW$近似已知会违反因果性，在复频率平面的上半平面产生具有非物理极点的自能。结合$GW$+DMFT的方法试图通过注入精确的局域自能来修复这一问题。利用最小Hubbard簇上的精确对角化，我们严格基准测试了$GW$和$GW$+DMFT自能的解析结构。我们展示了一个“二聚体异常”：在两位点二聚体上，反演对称性迫使非局域自能为纯实数，掩盖了因果性违反。转向非二部图的三位点Hubbard环，其中跳跃阻挫导致非局域自能具有有限虚部，我们证明了$GW$和$GW$+DMFT均违反Matsubara因果性条件。通过解析评估精确Lehmann矩，我们推导出自能高频尾部的闭式表达式$C = U^2\\,\mathrm{Var}(d)\\,I$，并表明标准方法无法捕获强制执行该表达式所需的精确等时双粒子关联函数。控制这一尾部的等时关联函数正是编码在完全不可约顶点$\Lambda$的高频渐近行为中的那些；然而，我们的中频分析表明，$GW$+DMFT中对$\Lambda$的仅局域截断留下了非局域RPA共振未修正。这两种诊断在逻辑上是独立的：$GW$+DMFT满足必要的高频条件$C\succeq0$，但在有限频率下仍违反Matsubara符号条件。以精确自能的无插值实轴评估作为主要因果性证书，并以有理延拓作为辅助证据，我们建立了一个严格的基准测试，表明在阻挫簇上，局域自能修正不足以保证因果解析结构。
英文摘要
The $GW$ approximation is known to violate causality, yielding self-energies with unphysical poles in the upper half of the complex frequency plane. The combined $GW$+DMFT approach attempts to cure this by injecting the exact local self-energy. Using exact diagonalization on minimal Hubbard clusters, we rigorously benchmark the analytic structure of the $GW$ and $GW$+DMFT self-energies. We demonstrate a ``dimer anomaly'': on the two-site dimer, inversion symmetry forces the non-local self-energy to be purely real, masking the causality violation. Moving to the non-bipartite three-site Hubbard ring, where hopping frustration yields a finite imaginary part in the non-local self-energy, we prove that both $GW$ and $GW$+DMFT violate the Matsubara causality condition. By analytically evaluating the exact Lehmann moments, we derive a closed-form expression for the high-frequency tail of the self-energy, $C = U^2\,\mathrm{Var}(d)\,I$, and show that standard methods fail to capture the exact equal-time two-particle correlators required to enforce it. The equal-time correlators that govern this tail are precisely those encoded in the high-frequency asymptotics of the fully irreducible vertex $Λ$; nevertheless, our intermediate-frequency analysis demonstrates that the local-only truncation of $Λ$ in $GW$+DMFT leaves non-local RPA resonances uncorrected. The two diagnostics are logically independent: $GW$+DMFT satisfies the necessary high-frequency condition $C\succeq0$ yet still violates the Matsubara sign condition at finite frequencies. Taking the interpolation-free real-axis evaluation of the exact self-energy as the primary causality certificate, with rational continuation as supporting evidence, we establish a rigorous benchmark demonstrating that local self-energy corrections are insufficient to guarantee a causal analytic structure on frustrated clusters.
CommentsA sign error in the polarization bubble of the accompanying code produced the reported causality violations in GW and GW+DMFT, so the paper's central claims, including the necessity of non-local vertex corrections, are incorrect.
