Operator evolution from the similarity renormalization group and the Magnus expansion

Abstract

The Magnus expansion is an efficient alternative to solving similarity renormalization group (SRG) flow equations with high-order, memory-intensive ordinary differential equation solvers. The numerical simplifications it offers for operator evolution are particularly valuable for in-medium SRG calculations, though challenges remain for difficult problems involving intruder states. Here we test the Magnus approach in an analogous but more accessible situation, which is the free-space SRG treatment of the spurious bound-states arising from a leading-order chiral effective field theory (EFT) potential with very high cutoffs. We show that the Magnus expansion passes these tests and then use the investigations as a springboard to address various aspects of operator evolution that have renewed relevance in the context of the scale and scheme dependence of nuclear processes. These aspects include SRG operator flow with band- versus block-diagonal generators, universality for chiral EFT Hamiltonians and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. Implications for short-range correlations physics and the possibilities for reconciling high- and low-resolution treatments of nuclear structure and reactions are discussed.

arXiv comment22 pages, 24 figures

References in corpus (45)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• The Magnus expansion and some of its applications
• The two-nucleon system at next-to-next-to-next-to-leading order
• Accurate nuclear radii and binding energies from a chiral interaction
• Model-independent low momentum nucleon interaction from phase shift equivalence
• From low-momentum interactions to nuclear structure
• Nuclear effective field theory: status and perspectives
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Renormalization of One-Pion Exchange and Power Counting
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Nucleon-Nucleon Correlations, Short-lived Excitations, and the Quarks Within
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Systematics of intermediate-energy single-nucleon removal cross sections
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• The Magnus expansion and the in-medium similarity renormalization group
• Delta isobars and nuclear saturation
• Probing the core of the strong nuclear interaction
• Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction
• The nuclear contacts and short range correlations in nuclei
• New applications of renormalization group methods in nuclear physics
• Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius
• Operator Evolution via the Similarity Renormalization Group I: The Deuteron
• New Ideas in Constraining Nuclear Forces
• Block Diagonalization using SRG Flow Equations
• Short-range correlations in nuclei with similarity renormalization group transformations
• Are low-energy nuclear observables sensitive to high-energy phase shifts?
• Operator evolution for ab initio nuclear theory
• High-momentum tails from low-momentum effective theories
• Scale dependence of deuteron electrodisintegration
• Can Long-Range Nuclear Properties Be Influenced By Short Range Interactions? A chiral dynamics estimate
• In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
• The impact of bound states on similarity renormalization group transformations
• How should one formulate, extract, and interpret `non-observables' for nuclei?
• Decoupling of Spurious Deep Bound States with the Similarity Renormalization Group
• Deuteron electrodisintegration with unitarily evolved potentials
• Global Properties of fp-Shell Interactions in Many-nucleon Systems
• Large-cutoff behavior of local chiral effective field theory interactions
• Program in C for studying characteristic properties of two-body interactions in the framework of spectral distribution theory
• Universality in Similarity Renormalization Group Evolved Potential Matrix Elements and T-Matrix Equivalence
• Tracing the evolution of nuclear forces under the similarity renormalization group

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• Short-range correlation physics at low RG resolution
• Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group
• High-resolution momentum distributions from low-resolution wave functions
• The quasi-deuteron model at low RG resolution
• Discovery vs. Precision in Nuclear Physics- A Tale of Three Scales
• Renormalization group evolution of optical potentials: explorations using a toy model
• Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions
• An overview of symmetric nuclear matter properties from chiral interactions up to fourth order of the chiral expansion