Low-rank matrix decompositions for ab initio nuclear structure

TL;DR

This paper introduces matrix factorization techniques to reduce computational costs in ab initio nuclear structure calculations, enabling more efficient handling of large data objects in many-body quantum systems.

Contribution

It presents a systematic approach using low-rank matrix decompositions to improve computational efficiency in nuclear many-body methods, applicable to various nuclear systems.

Findings

Reduced computational cost in nuclear two-body systems

Effective application in many-body perturbation theory

Successful implementation in in-medium similarity renormalization group simulations

Abstract

The extension of ab initio quantum many-body theory to higher accuracy and larger systems is intrinsically limited by the handling of large data objects in form of wave-function expansions and/or many-body operators. In this work we present matrix factorization techniques as a systematically improvable and robust tool to significantly reduce the computational cost in many-body applications at the price of introducing a moderate decomposition error. We demonstrate the power of this approach for the nuclear two-body systems, for many-body perturbation theory calculations of symmetric nuclear matter, and for non-perturbative in-medium similarity renormalization group simulations of finite nuclei. Establishing low-rank expansions of chiral nuclear interactions offers possibilities to reformulate many-body methods in ways that take advantage of tensor factorization strategies.