Dimensionality reduction through tensor factorization: Application to ab initio nuclear physics calculations

¹ CEA, DES, IRESNE, DER, SPRC, LEPh, 13115 Saint-Paul-lez-Durance, France
² IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
³ KU Leuven, Department of Physics and Astronomy, Instituut vor Kern- en Stralingsfysica, 3001 Leuven, Belgium
⁴ CEA, DAM, DIF, 91297 Arpajon, France
⁵ Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680 Bruyères-le-Châtel, France

^* e-mail: mikael.frosini@cea.fr
^** e-mail: thomas.duguet@cea.fr
^*** e-mail: pierre.tamagno@cea.fr
^**** e-mail: lars.zurek@cea.fr

Published online: 15 October 2024

Abstract

The construction of predictive models of atomic nuclei from first principles is a challenging (yet necessary) task towards the systematic generation of theoretical predictions (and associated uncertainties) to support nuclear data evaluation. The consistent description of the rich phenomenology of nuclear systems indeed requires the introduction of reductionist approaches that construct nuclei directly from interacting nucleons by solving the associated quantum many-body problem. In this context, so-called ab initio methods offer a promising route by deriving controlled (and systematically improvable) approximations both to the inter-nucleon interaction and to the solutions of the many-body problem. From a technical point of view, approximately solving the many-body Schrödinger equation in heavy open-shell systems typically requires the construction and contraction of large mode-4 (mode-6) tensors that need to be stored repeatedly. Recently, a new dimensionality reduction method based on randomized singular value decomposition has been introduced to reduce the numerical cost of many-body perturbation theory. This work applies this lightweight formalism to the study of the Germanium isotopic chain, where standard approaches would be too expansive to run. Inclusion of triaxiality is found to improve the overall agreement with experimental data on differential quantities.