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

Abstract

The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schrödinger 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.

7 pages, 3 figures, 2 tables

References in corpus (23)

• Improved nuclear matter calculations from chiral low-momentum interactions
• A nucleus-dependent valence-space approach to nuclear structure
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• In-Medium Similarity Renormalization Group for Nuclei
• Coupled-cluster calculations of neutrinoless double-beta decay in ${}^{48}$Ca
• Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei
• In-medium similarity renormalization group with three-body operators
• Ab initio uncertainty quantification of neutrinoless double-beta decay in ${}^{76}$Ge
• \texttt{NuHamil}: A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory
• Impact of two-body currents on magnetic dipole moments of nuclei
• Probing new bosons and nuclear structure with ytterbium isotope shifts
• Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory
• Ab initio structure factors for spin-dependent dark matter direct detection
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Improved structure of calcium isotopes from ab initio calculations
• An $\text{ab initio}$ strategy for taming nuclear-structure dependence of $V_{ud}$ extractions: the ${}^{10}\mathrm{C}\to {}^{10}\mathrm{B}$ superallowed transition
• Factorized Approximation to the IMSRG(3)
• IMSRG with flowing 3 body operators, and approximations thereof
• Ab initio calculations of overlap integrals for $\mu \to e$ conversion in nuclei
• Ab initio computations of the fourth-order charge density moments of ${}^{48}$Ca and ${}^{208}$Pb
• Computing nuclear response functions with time-dependent coupled-cluster theory
• Nuclear Schiff moment of fluorine isotope ${}^{19}$F