In-medium $k$-body reduction of $n$-body operators

TL;DR

This paper introduces a new approximation technique for reducing the computational complexity of three-nucleon interactions in nuclear structure calculations, achieving high accuracy across various nuclei and methods.

Contribution

A simple, universal, and accurate approximation method for in-medium $k$-body reduction of $n$-body operators using a symmetry-invariant one-body matrix.

Findings

Errors below 2-3% across many nuclei and observables

Effective for low-resolution Hamiltonians

Applicable to various many-body methods

Abstract

The computational cost of ab initio nuclear structure calculations is rendered particularly acute by the presence of (at least) three-nucleon interactions. This feature becomes especially critical now that many-body methods aim at extending their reach beyond mid-mass nuclei. Consequently, state-of-the-art ab initio calculations are typically performed while approximating three-nucleon interactions in terms of effective, i.e. system-dependent, zero-, one- and two-nucleon operators. While straightforward in doubly closed-shell nuclei, existing approximation methods based on normal-ordering techniques involve either two- and three-body density matrices or a symmetry-breaking one-body density matrix in open-shell systems. In order to avoid such complications, a simple, flexible, universal and accurate approximation technique involving the convolution of the initial operator with a sole symmetry-invariant one-body matrix is presently formulated and tested numerically. Employed with a low-resolution Hamiltonian, the novel approximation method is shown to induce errors below $2-3\%$ across a large range of nuclei, observables and many-body methods.