https://doi.org/10.1140/epja/s10050-024-01397-1
Regular Article –Theoretical Physics
Tensor factorization in ab initio many-body calculations
Triaxially-deformed (B)MBPT calculations in large bases
1
CEA, DES, IRESNE, DER, SPRC, LEPh, 13108, Saint-Paul-lez-Durance, France
2
IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
3
Department of Physics and Astronomy, KU Leuven, Instituut voor Kern-en Stralingsfysica, 3001, Leuven, Belgium
Received:
12
April
2024
Accepted:
10
August
2024
Published online:
14
September
2024
Whether for fundamental studies or nuclear data evaluations, first-principle calculations of atomic nuclei constitute the path forward. Today, performing ab initio calculations (a) of heavy nuclei, (b) of doubly open-shell nuclei or (c) with a sub-percent accuracy is at the forefront of nuclear structure theory. While combining any two of these features constitutes a major challenge, addressing the three at the same time is currently impossible. From a numerical standpoint, these challenges relate to the necessity to handle (i) very large single-particle bases and (ii) mode-6, i.e. three-body, tensors (iii) that must be stored repeatedly. Performing second-order many-body perturbation theory(ies) calculations based on triaxially deformed and superfluid reference states of doubly open-shell nuclei up to mass 
, the present work achieves a significant step forward by addressing challenge (i). To do so, the memory and computational cost associated with the handling of large tensors is scaled down via the use of tensor factorization techniques. The presently used factorization format is based on a randomized singular value decomposition that does not require the computation and storage of the very large initial tensor. The procedure delivers an inexpensive and controllable approximation to the original problem, as presently illustrated for calculations that could not be performed without tensor factorization. With the presently developed technology at hand, one can envision to perform calculations of yet heavier doubly open-shell nuclei at sub-percent accuracy in a foreseeable future.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
