论文标题
削减规则和阳性在有限温度多体理论中
Cutting rules and positivity in finite temperature many-body theory
论文作者
论文摘要
对于多体扰动理论中给定的示意图近似，不能保证诸如密度或光谱函数之类的积极可观察物保持其阳性。对于零温度系统，我们开发了一种基于Feynman图的所谓切割规则的方法[Phys.Rev.B 90,115134（2014）]，该方法对这些特性进行了示意，从而解决了对各种Verterex近似值观察到的负光谱密度的问题。在这项工作中，我们通过以迟滞的$ n $ - 点功能制定切割规则，将此方法扩展到有限温度的系统，从而简化了早期的方法并同时求解了困扰有限温度膨胀的不变真空图的问题。此外，我们的方法对于初始平衡的非平衡系统是有效的，并且使我们能够证明重要的是使用近似值，即$ GW $，第二个出生和$ t $ -matrix近似值，在有限温度下保留正频谱功能。最后，我们得出了智障$ n $ point功能的光谱形式与其Matsubara对应物的分析性延续关系，以及一套Feynman规则来评估它们。
For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For zero-temperature systems we developed a method [Phys.Rev.B 90,115134 (2014)] based on so-called cutting rules for Feynman diagrams that enforces these properties diagrammatically, thus solving the problem of negative spectral densities observed for various vertex approximations. In this work we extend this method to systems at finite temperature by formulating the cutting rules in terms of retarded $N$-point functions, thereby simplifying earlier approaches and simultaneously solving the issue of non-vanishing vacuum diagrams that has plagued finite temperature expansions. Our approach is moreover valid for nonequilibrium systems in initial equilibrium and allows us to show that important commonly used approximations, namely the $GW$, second Born and $T$-matrix approximation, retain positive spectral functions at finite temperature. Finally we derive an analytic continuation relation between the spectral forms of retarded $N$-point functions and their Matsubara counterparts and a set of Feynman rules to evaluate them.
