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

Autor: Thomas Duguet, P. Arthuis, R. D. Lasseri, Alexander Tichai, Jean-Paul Ebran
Přispěvatelé: Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut de Physique Nucléaire d'Orsay (IPNO), Université Paris-Sud - Paris 11 (UP11)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11)
Rok vydání: 2019
Předmět:
Nuclear Theory
[PHYS.NUCL]Physics [physics]/Nuclear Theory [nucl-th]
Atomic Physics (physics.atom-ph)
Computer science
FOS: Physical sciences
General Physics and Astronomy
Perturbation theory
01 natural sciences
Physics - Atomic Physics
010305 fluids & plasmas
Nuclear Theory (nucl-th)
Condensed Matter - Strongly Correlated Electrons
symbols.namesake
Physics - Chemical Physics
0103 physical sciences
Feynman diagram
Adjacency matrix
Algebraic number
Algebraic expression
010306 general physics
Feynman diagrams
Chemical Physics (physics.chem-ph)
Many-body theory
[PHYS]Physics [physics]
Strongly Correlated Electrons (cond-mat.str-el)
ab initio
21.60.De
Graph theory
[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]
Algebra
Diagrammatic reasoning
Hardware and Architecture
symbols
Perturbation theory (quantum mechanics)
Tuple
Zdroj: Comput.Phys.Commun.
Comput.Phys.Commun., 2019, 240, pp.202-227. ⟨10.1016/j.cpc.2018.11.023⟩
ISSN: 0010-4655
Popis: 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. 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 at play in various many-body formalisms that already exist or are yet to be formulated.
32 pages, 22 figures, 6 tables
Databáze: OpenAIRE
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