从弱耦合到强耦合的局部顶点修正的参数化：Hedin三支顶点的重要性
Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
摘要：
在关联系统的研究中，基于动力学平均场论（DMFT）的近似方法提供了一种考虑局部顶点修正的实用方法，它分别描述了弱耦合时粒子-粒子屏蔽和强耦合时局部矩的形成。我们表明，在这两个限制的本地顶点校正可以有效地参数化单玻色子交换，这样的DMFT和它的图形扩展描述的两粒子物理恢复到良好的近似，并在降低计算成本。我们的调查强调了频率相关的费米子玻色子耦合（赫丁顶点）的局部顶点校正的重要性。也就是说，在弱耦合时，与静态平均场相比，费米子-自旋-玻色子耦合抑制了DMFT近似的Néel温度，而对于大的相互作用，它促进了局域自旋涨落交换的巨大增强，产生了有效交换能标$4t^2/U$。我们发现，忽略费米子-玻色子耦合的非平凡部分的顶点的参数化定性失败在强耦合。
英文摘要：
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 to 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.
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