ADG: automated generation and evaluation of many-body diagrams

Tichai, A.; Arthuis, P.; Hergert, H.; Duguet, T.

doi:10.1140/epja/s10050-021-00621-6

Title: ADG: automated generation and evaluation of many-body diagrams

Journal Article · 10 January 2022 · European Physical Journal. A

DOI: https://doi.org/10.1140/epja/s10050-021-00621-6 · OSTI ID:1980784

Tichai, A. ^[1]; Arthuis, P. ^[2]; Hergert, H. ^[3]; Duguet, T. ^[4]

Technical University of Darmstadt (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt (Germany); Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, Heidelberg (Germany); OSTI
Technical University of Darmstadt (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt (Germany)
Michigan State University, East Lansing, MI (United States)
University Paris-Saclay, Gif-sur-Yvette (France); Katholieke University Leuven (Belgium)

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green’s function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

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Research Organization:: Michigan State University, East Lansing, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); German Research Foundation (DFG); Max Planck Society; Federal Ministry of Education and Research (BMBF); National Science Foundation (NSF)

Grant/Contract Number:: SC0017887

OSTI ID:: 1980784

Journal Information:: European Physical Journal. A, Journal Name: European Physical Journal. A Journal Issue: 1 Vol. 58; ISSN 1434-6001

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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