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Article Dans Une Revue Comput.Phys.Commun. Année : 2019

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

Résumé

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)×(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. The diagrammatic rule in question constitutes a novel finding allowing for the straight summation of large classes of time-ordered diagrams at play in the time-independent formulation of BMBPT. Correspondingly, the traditional resolvent rule employed to compute time-ordered diagrams happens to be a particular case of the general rule presently identified. The code ADG is written in Python2.7 and uses the graph manipulation package NetworkX . The code is also able to generate and evaluate Hartree–Fock-MBPT (HF-MBPT) diagrams and is made flexible enough to be expanded throughout the years to tackle the diagrammatics used in various many-body formalisms that already exist or are yet to be formulated.
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Dates et versions

hal-01880793 , version 1 (25-10-2021)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

Citer

P. Arthuis, T. Duguet, A. Tichai, R.-D. Lasseri, J.-P. Ebran. ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory. Comput.Phys.Commun., 2019, 240, pp.202-227. ⟨10.1016/j.cpc.2018.11.023⟩. ⟨hal-01880793⟩
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