ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory

We describe the second version (v2.0.0) of code ADG that automatically (1) generates all valid off-diagonal Bogoliubov many-body perturbation theory diagrams at play in particle-number projected (PNP-BMBPT) and (2) evaluates their algebraic expression to be implemented for numerical applications. This is achieved any perturbative order p a Hamiltonian containing both two-body (four-legs) three-body (six-legs) interactions (vertices). All BMBPT are systematically generated from set diagonal, i.e.,unprojected, diagrams. The production latter were described length Arthuis et al. (2019) dealing with first ADG. automated evaluation relies on application Feynman’s rules identification powerful diagrammatic rule providing result remaining p-tuple time integral. new generalizes one already identified evaluate diagonal independently topology. written Python3 uses graph manipulation package NetworkX. kept flexible enough further expanded throughout years tackle diagrammatics various formalisms exist or yet formulated. Program Title: CPC Library link program files: https://doi.org/10.17632/6h4xrydwfb.2 Licensing provisions: GPLv3 Programming language: Journal reference previous version: P. Arthuis, T. Duguet, A. Tichai, R.-D. Lasseri J.-P. Ebran, ”ADG: Automated generation I. theory”, Computer Physics Communications 240 (2019), pp. 202-227. Does supersede version?: Yes. Reasons Incorporation formalism into program. Summary revisions: Addition which can generated, fix wrong symmetry factor, move codebase Python2 while maintaining support Python2, optimizations reduce memory necessary Nature problem: As formal developments many-body-perturbation-theory-based ab initio methods make higher orders reachable, manually producing evaluating becomes rapidly untractable as number complexity grow quickly, making it prone mistakes oversights. Solution method: Diagonal encoded square matrices known oriented adjacency theory, then turned objects using NetworkX package. Off-diagonal those graphs. Checks time-integrated eventually done purely basis. HF-MBPT produced evaluated well same principle.