Datensatz

Zusammenfassung

We describe the second version (v2.0.0) of the code ADG that
automatically (1) generates all valid off-diagonal Bogoliubov many-body
perturbation theory diagrams at play in particle-number projected
Bogoliubov many-body perturbation theory (PNP-BMBPT) 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). All valid off-diagonal BMBPT diagrams of order
p are systematically generated from the set of diagonal, i.e.,
unprojected, BMBPT diagrams. The production of the latter were described
at length in Arthuis et al. (2019) dealing with the first version of
ADG. The automated evaluation of off-diagonal BMBPT diagrams 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 new diagrammatic rule
generalizes the one already identified in Arthuis et al. (2019) to
evaluate diagonal BMBPT diagrams independently of their perturbative
order and topology. The code ADG is written in Python3 and uses the
graph manipulation package NetworkX. The code is kept flexible enough to
be further expanded throughout the years to tackle the diagrammatics at
play in various many-body formalisms that already exist or are yet to be
formulated.
Program summary
Program Title: ADG
CPC Library link to program files: http://doi.org/10.17632/6h4xrydwfb.2
Licensing provisions: GPLv3
Programming language: Python3
Journal reference of previous version: P. Arthuis, T. Duguet, A. Tichai,
R.-D. Lasseri and J.-P. Ebran, "ADG: Automated generation and evaluation
of many-body diagrams I. Bogoliubov many-body perturbation theory',
Computer Physics Communications 240 (2019), pp. 202-227.
Does the new version supersede the previous version?: Yes.
Reasons for the new version: Incorporation of a new formalism into the
program.
Summary of revisions: Addition of off-diagonal BMBPT to the formalisms
for which diagrams can be generated, fix of a wrong symmetry factor,
move of the codebase from Python2 to Python3 while maintaining support
for Python2, various optimizations to reduce the time and memory
necessary to the program.
Nature of problem: As formal and numerical developments in
many-body-perturbation-theory-based ab initio methods make higher orders
reachable, manually producing and evaluating all the diagrams becomes
rapidly untractable as both their number and complexity grow quickly,
making it prone to mistakes and oversights.
Solution method: Diagonal BMBPT diagrams are encoded as square matrices
known as oriented adjacency matrices in graph theory, and then turned
into graph objects using the NetworkX package. Off-diagonal BMBPT
diagrams can then be generated from those graphs. Checks on the diagrams
and evaluation of their time-integrated expression are eventually done
on a purely diagrammatic basis. HF-MBPT diagrams are produced and
evaluated as well using the same principle. (C) 2020 Elsevier B.V. All
rights reserved.