Improved many-body expansions from eigenvector continuation

TL;DR

This paper introduces eigenvector continuation as an effective resummation method to improve the convergence of many-body expansions in quantum systems, especially where traditional perturbation theory struggles due to strong interactions.

Contribution

It proposes eigenvector continuation as a new, mathematically simple resummation technique that enhances the accuracy and reliability of many-body calculations in complex quantum systems.

Findings

Eigenvector continuation improves convergence in many-body expansions.

The method is efficient and reliable across various quantum systems.

It offers an alternative to traditional resummation schemes.

Abstract

Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment of microscopic fermionic systems, it is desirable to obtain accurate results through low-order perturbation theory. In atomic nuclei however, effects such as strong short-range repulsion between nucleons can spoil the convergence of the expansion and make the reliability of perturbation theory unclear. Mathematicians have devised an extensive machinery to overcome the problem of divergent expansions by making use of so-called resummation methods. In large-scale many-body applications such schemes are often of limited use since no a priori analytical knowledge of the expansion is available. We present here eigenvector continuation as an alternative resummation tool that is both efficient and reliable because it is based on robust and simple mathematical principles.