Counting Feynman diagrams via many-body relations

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.

References in corpus (3)

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Multiloop functional renormalization group for general models
• Hedin's equations and enumeration of Feynman's diagrams

Cited by in corpus (7)

• Derivation of exact flow equations from the self-consistent parquet relations
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• A recursive enumeration of connected Feynman diagrams with an arbitrary number of external legs in the fermionic non-relativistic interacting gas
• Seven Etudes on dynamical Keldysh Model
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model