Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 Munich, Germany.
Phys Rev E. 2018 Aug;98(2-1):023303. doi: 10.1103/PhysRevE.98.023303.
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction. Further, we apply it to different parquet-type approximations and consider spin-resolved diagrams in the Hubbard model. Low-order results and asymptotics are explicitly discussed for various vertex functions and different two-particle channels. The algorithm can easily be implemented and generalized to many-body relations of different forms and levels of approximation.
我们提出了一种通过多体关系来计算费曼图的迭代算法。该算法允许我们在相互作用的每阶计算一般费米子多体问题的确切解的图的数量。此外，我们将其应用于不同的准粒子型近似，并在 Hubbard 模型中考虑自旋分辨图。对于各种顶点函数和不同的双粒子通道，我们明确讨论了低阶结果和渐近性。该算法可以很容易地实现和推广到不同形式和近似水平的多体关系。
