The nuclear matter equation-of-state (NM-EOS) determines the stability and bulk properties of nuclear matter, and is thus, directly linked to astrophysical phenomena—e.g., neutron star physics. Moreover, a tightly constrained NM-EOS opens an avenue to test and improve nuclear force models. The NM-EOS is therefore of great interest to the physics community. Recent advances in ab initio nuclear theory have led to an explosion of nuclear forces amenable to many-body methods that scale polynomially in time. Some of such methods include Many-Body Perturbation Theory (MBPT), and non-perturbative approaches: In-Medium Similarity Renormalization Group (IMSRG), and Coupled-Cluster (CC) theory. Unlike MBPT and CC, the IMSRG has not been applied to study NM-EOS with realistic nucleon forces. Therefore, we apply the IMSRG to calculate NM-EOS using multiple realistic forces. To accomplish this goal, we develop a state-of-the-art, high-performant nuclear matter IMSRG program with access to a multitude of two- and three-body nuclear forces. We compare NM-EOS obtained from MBPT, IMSRG, and CC to benchmark the methods. And we observe notable disparities between the methods in symmetric nuclear matter that are due to non-perturbative physics. IMSRG NM-EOS computations are done at scale, and are therefore, highly computationally demanding. Consequently, we introduce novel ideas to accelerate IMSRG computations using Unitary Coupled-Cluster (UCC)-inspired IMSRG generators, and Shanks and Padé IMSRG extrapolators. We realize that approximate UCC solutions can be used as IMSRG generators. And, viewing UCC as a nonlinear commutator inversion problem, we realize that UCC amplitudes are given by a generalized Born series—so long the series converges. Using these developments, we introduce three IMSRG generators named “Born,” “UCC-Born,” and “Carinae.” Using the novel generators, we sometimes observe 2–4X IMSRG speedup, particularly when the IMSRG is slowly convergent.
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