Dimensionality reduction through tensor factorization : application to \textit{ab initio} nuclear physics calculations

TL;DR

This paper introduces a tensor factorization method using randomized singular value decomposition to reduce computational costs in ab initio nuclear physics calculations, enabling analysis of heavier nuclei like Germanium isotopes.

Contribution

It applies a novel dimensionality reduction technique to ab initio nuclear models, improving efficiency and allowing study of complex nuclei previously too computationally demanding.

Findings

Dimensionality reduction decreases computational costs significantly.

Including triaxiality improves agreement with experimental data.

Method enables analysis of heavier isotopes like Germanium.

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 \textit{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 Schr\"odinger 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.