IMSRG with flowing 3 body operators, and approximations thereof

TL;DR

This paper investigates the effects of including three-body operators in the IMSRG method and finds that a specific approximation scheme closely matches the full treatment, improving computational efficiency.

Contribution

The study introduces an approximation scheme for IMSRG that retains key three-body operator contributions with minimal computational cost.

Findings

Retaining N^7 scaling commutators approximates full three-body treatment well.

The approximation scheme is effective in toy models and in nuclear isotope calculations.

The approach enhances IMSRG accuracy with reduced computational complexity.

Abstract

We explore the impact of retaining three-body operators within the in-medium similarity renormalization group (IMSRG), as well as various approximations schemes. After studying two toy problems, idential fermions with a contact interaction and the Lipkin-Meshkov-Glick model, we employ the valence-space formulation of the IMSRG to investigate the even-$A$ carbon isotopes with a chiral two-body potential. We find that retaining only those commutators expressions that scale as $N^7$ provides an excellent approximation of the full three-body treatment.