Singular value decomposition and similarity renormalization group evolution of nuclear interactions

Zhu, B.; Wirth, R.; Hergert, H.

doi:10.1103/physrevc.104.044002

Singular value decomposition and similarity renormalization group evolution of nuclear interactions

Journal Article · Mon Oct 11 00:00:00 EDT 2021 · Physical Review. C

DOI:https://doi.org/10.1103/physrevc.104.044002· OSTI ID:1962726

Zhu, B. ^[1]; ^[2]; ^[2]

Michigan State Univ., East Lansing, MI (United States); Facility for Rare Isotope Beams, Michigan State University
Michigan State Univ., East Lansing, MI (United States)

One of the main challenges for ab initio nuclear many-body theory is the growth of computational and storage costs as calculations are extended to heavy, exotic, and structurally complex nuclei. Here, we investigate the factorization of nuclear interactions as a means to address this issue. We perform Singular Value Decompositions of nucleon-nucleon interactions in partial wave representation and study the dependence of the singular value spectrum on interaction characteristics like regularization scheme and resolution scales. We develop and implement the Similarity Renormalization Group (SRG) evolution of the factorized interaction, and demonstrate that this SVD-SRG approach accurately preserves two-nucleon observables. We find that low-resolution interactions allow the truncation of the SVD at low rank, and that a small number of relevant components is sufficient to capture the nuclear interaction and perform an accurate SRG evolution, while the Coulomb interaction requires special consideration. The rank is uniform across all partial waves, and almost independent of the basis choice in the tested cases. This suggests an interpretation of the relevant singular components as mere representations of a small set of abstract operators that can describe the interaction and its SRG flow. Following the traditional workflow for nuclear interactions, we discuss how the transformation between the center-of-mass and laboratory frames creates redundant copies of the partial wave components when implemented in matrix representation, and we discuss strategies for mitigation. Lastly, we test the low-rank approximation to the SRG-evolved interactions in many-body calculations using the In-Medium SRG. By including nuclear radii in our analysis, we verify that the implementation of the SRG using the singular vectors of the interaction does not spoil the evolution of other observables.

View Accepted Manuscript (DOE)

Research Organization:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0017887; SC0018083

OSTI ID:: 1962726

Journal Information:: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 4 Vol. 104; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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References (73)

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