Counting Feynman diagrams via many-body relations

Fabian B. Kugler

doi:10.1103/physreve.98.023303

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arXiv · 1808.01759

Counting Feynman diagrams via many-body relations

Fabian B. Kugler

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Abstract

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.

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Fabian B. Kugler. 2018-08-06. Counting Feynman diagrams via many-body relations. https://doi.org/10.1103/physreve.98.023303

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