Computational schemes for the Magnus expansion of the in-medium similarity renormalization group

TL;DR

This paper investigates the accuracy and uncertainties of a computational scheme for the IMSRG method, comparing it to standard approaches and assessing its effectiveness in capturing three-body effects in nuclear calculations.

Contribution

It provides an analysis of the hunter-gatherer scheme's uncertainty in IMSRG(3) approximations, highlighting its potential and limitations.

Findings

Hunter-gatherer scheme differs by up to 7 MeV in ground-state energies.

Differences of up to 0.5 MeV in excitation energies compared to standard IMSRG(2).

Uncertainties are comparable to expected IMSRG(3) corrections.

Abstract

The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schr\"odinger equation through a continuous unitary transformation of the many-body Hamiltonian. The IMSRG transformation is typically truncated at the normal-ordered two-body level, the IMSRG(2), but recently several approaches have been developed to capture the effects of normal-ordered three-body operators, the IMSRG(3). In particular, a factorized approximation to the IMSRG(3) proposes to capture the leading effects of three-body operators at the same computational cost as the IMSRG(2) approximation. This approach often employs an approximate scheme for solving the IMSRG equations, the so-called hunter-gatherer scheme. In this work, I study the uncertainty associated with this scheme. I find that the hunter-gatherer scheme differs by up to $7\,\mathrm{MeV}$ for ground-state energies and $0.5\,\mathrm{MeV}$ for excitation energies from standard IMSRG(2) approaches. These differences are in some cases comparable to the expected size of IMSRG(3) corrections.