In-medium similarity renormalization group with three-body operators

TL;DR

This paper extends the in-medium similarity renormalization group (IMSRG) method to include three-body operators, improving accuracy in nuclear structure calculations while proposing computationally feasible truncations.

Contribution

The work introduces the IMSRG(3) approach, incorporating three-body operators, and develops truncation schemes to approximate it efficiently, enhancing the method's accuracy.

Findings

IMSRG(3) systematically improves over IMSRG(2) for nuclear calculations.

Approximate IMSRG(3) truncations reproduce systematic improvements.

Truncation strategies behave consistently with perturbative analysis.

Abstract

Over the past decade the in-medium similarity renormalization group (IMSRG) approach has proven to be a powerful and versatile ab initio many-body method for studying medium-mass nuclei. So far, the IMSRG was limited to the approximation in which only up to two-body operators are incorporated in the renormalization group flow, referred to as the IMSRG(2). In this work, we extend the IMSRG(2) approach to fully include three-body operators yielding the IMSRG(3) approximation. We use a perturbative scaling analysis to estimate the importance of individual terms in this approximation and introduce truncations that aim to approximate the IMSRG(3) at a lower computational cost. The IMSRG(3) is systematically benchmarked for different nuclear Hamiltonians for ${}^{4}\text{He}$ and ${}^{16}\text{O}$ in small model spaces. The IMSRG(3) systematically improves over the IMSRG(2) relative to exact results. Approximate IMSRG(3) truncations constructed based on computational cost are able to reproduce much of the systematic improvement offered by the full IMSRG(3). We also find that the approximate IMSRG(3) truncations behave consistently with expectations from our perturbative analysis, indicating that this strategy may also be used to systematically approximate the IMSRG(3).