{\it Ab initio} nuclear structure - the large sparse matrix eigenvalue problem

TL;DR

This paper reviews recent progress in solving large sparse matrix eigenvalue problems in ab initio nuclear structure calculations, highlighting computational challenges and future directions for understanding light nuclei.

Contribution

It surveys advances in computational methods for large sparse eigenvalue problems in ab initio nuclear physics, emphasizing recent results and future challenges.

Findings

Eigenvalue problems often exceed 10^10 matrix dimensions.

Recent methods enable nearly exact solutions for some nuclear properties.

Computational challenges include storage and processing of large sparse matrices.

Abstract

The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several {\it ab initio} methods have now emerged that provide nearly exact solutions for some nuclear properties. The {\it ab initio} no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds $10^{10}$ and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. W also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these {\it ab initio} approaches.