Importance truncation for the in-medium similarity renormalization group

Abstract

Ab initio nuclear many-body frameworks require extensive computational resources, especially when targeting heavier nuclei. Importance-truncation (IT) techniques allow to significantly reduce the dimensionality of the problem by neglecting unimportant contributions to the solution of the many-body problem. In this work, we apply IT methods to the nonperturbative in-medium similarity renormalization group (IMSRG) approach and investigate the induced errors for ground-state energies in different mass regimes based on different nuclear Hamiltonians. We study various importance measures, which define the IT selection, and identify two measures that perform best, resulting in only small errors to the full IMSRG(2) calculations even for sizable compression ratios. The neglected contributions are accounted for in a perturbative way and serve as an estimate of the IT-induced error. Overall we find that the IT-IMSRG(2) performs well across all systems considered, while the largest compression ratios for a given error can be achieved when using soft Hamiltonians and for large single-particle bases.

arXiv comment14 pages, 9 figures, published version

References in corpus (45)

• Quantum Monte Carlo methods for nuclear physics
• Improved nuclear matter calculations from chiral low-momentum interactions
• Coupled-cluster computations of atomic nuclei
• Self-consistent Green's function method for nuclei and nuclear matter
• From low-momentum interactions to nuclear structure
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• Quantifying truncation errors in effective field theory
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• In-Medium Similarity Renormalization Group for Nuclei
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Structure of the lightest tin isotopes
• Ab initio limits of atomic nuclei
• Importance Truncation for Large-Scale Configuration Interaction Approaches
• Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions
• Ab Initio Path to Heavy Nuclei
• Novel chiral Hamiltonian and observables in light and medium-mass nuclei
• The Magnus expansion and the in-medium similarity renormalization group
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Converged ab initio calculations of heavy nuclei
• A User-Friendly Hybrid Sparse Matrix Class in C++
• Charge radii of exotic neon and magnesium isotopes
• Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
• Properties of nuclei up to $A=16$ using local chiral interactions
• Evolved Chiral NN+3N Hamiltonians for Ab Initio Nuclear Structure Calculations
• Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• Coupled-cluster calculations of neutrinoless double-beta decay in ${}^{48}$Ca
• Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
• In-medium similarity renormalization group with three-body operators
• Natural orbitals for ab initio no-core shell model calculations
• Probing chiral interactions up to next-to-next-to-next-to-leading order in medium-mass nuclei
• Charge radius of the short-lived ${}^{68}$Ni and correlation with the dipole polarizability
• In-medium $k$-body reduction of $n$-body operators
• BIGSTICK: A flexible configuration-interaction shell-model code (updated)
• Natural orbitals for many-body expansion methods
• Role of chiral two-body currents in ${}^6$Li magnetic properties in light of a new precision measurement with the relative self-absorption technique
• Normal-ordered $k$-body approximation in particle-number-breaking theories
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Importance truncation in non-perturbative many-body techniques

Cited by in corpus (3)

• Least-square approach for singular value decompositions of scattering problems
• NuLattice: Ab initio computations of atomic nuclei on lattices
• Deformed natural orbitals for ab initio calculations