In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parametrized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion–spin-boson coupling suppresses the Néel temperature of the DMFT approximation compared with the static mean field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale $4t^2/U$. We find that parametrizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.

中文翻译：

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从弱耦合到强耦合的局部顶点校正的参数化：Hedin 三腿顶点的重要性

在相关系统的研究中，基于动态平均场理论 (DMFT) 的近似提供了一种考虑局部顶点校正的实用方法，分别捕获弱耦合下的粒子 - 粒子筛选和局部矩的形成在强耦合。我们表明，在这两个限制中，局部顶点校正可以根据单玻色子交换有效地参数化，从而使 DMFT 描述的双粒子物理及其图解扩展恢复到良好的近似值并降低计算成本。我们的研究强调了频率相关费米子-玻色子耦合（Hedin 顶点）对于局部顶点校正的重要性。即，$4{吨}^2/你$. 我们发现忽略费米子-玻色子耦合的重要部分的顶点参数化在强耦合下定性失败。