In-medium similarity renormalization group with three-body operators

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).

23 pages, 10 figures, published version

References in corpus (10)

• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Accurate nuclear radii and binding energies from a chiral interaction
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• In-Medium Similarity Renormalization Group for Nuclei
• Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
• Coupled-cluster theory for three-body Hamiltonians
• Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes
• Momentum space evolution of chiral three-nucleon forces
• Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

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