自洽多体微扰论的物理与非物理区域
Physical and unphysical regimes of self-consistent many-body perturbation theory
AI总结：
研究自洽多体微扰论中截断自能级数的收敛性，证明弱耦合下收敛至精确传播子而强耦合下偏离，并提出无需精确解即可区分物理与非物理区域的判据。
摘要：
在自洽多体微扰论的标准框架中，自能的骨架级数被截断至有限阶$\mathcal{N}$，并代入戴森方程，随后求解传播子$G_{\mathcal{N}}\\,$。我们考虑两个费米子模型实例：半填充的哈伯德原子及其零时空维简化版本。首先，我们证明当$\mathcal{N}\to\infty$时，$G_{\mathcal{N}}\\,$收敛至极限$G_\infty\\,$，在耦合足够弱时，该极限与精确物理传播子$G_{\rm exact}\\ $一致，而在强耦合时$G_\infty \neq G_{\rm exact}\\ $。这源于[Kozik, Ferrero and Georges, PRL 114, 156402 (2015)]的发现以及此处阐明的一个微妙数学机制。其次，我们证明，借助一个无需知道$G_{\rm exact}\\ $的判据，可以区分$G_\infty=G_{\rm exact}\\ $与$G_\infty\neq G_{\rm exact}\\ $两种区域，如[Rossi et al., PRB 93, 161102(R) (2016)]所提议。
英文摘要：
In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $\mathcal{N}$ and plugged into the Dyson equation, which is then solved for the propagator $G_{\mathcal{N}}\,$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_{\mathcal{N}}\,$ converges when $\mathcal{N}\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}\ $ at small enough coupling, while $G_\infty \neq G_{\rm exact}\ $ at strong coupling. This follows from the findings of [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}\ $ and $G_\infty\neq G_{\rm exact}\ $ regimes thanks to a criterion which does not require the knowledge of $G_{\rm exact}\ $, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)].
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