ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory

Understand

We describe the first version (v1.0.0) of the code ADG that automatically (1) generates all valid Bogoliubov many-body perturbation theory (BMBPT) diagrams and (2) evaluates their algebraic expression to be implemented for numerical applications.

• This is achieved at any perturbative order $p$ for a Hamiltonian containing both two-body (four-legs) and three-body (six-legs) interactions (vertices).
• The automated generation of BMBPT diagrams of order $p$ relies on elements of graph theory, i.e., it is achieved by producing all oriented adjacency matrices of size $(p+1) \times (p+1)$ satisfying topological Feynman's rules.
• The automated evaluation of BMBPT diagrams of order $p$ relies both on the application of algebraic Feynman's rules and on the identification of a powerful diagrammatic rule providing the result of the remaining $p$-tuple time integral.