Singular value decomposition and similarity renormalization group evolution of nuclear interactions
Abstract
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 transformationmore »
- Publication Date:
- Research Org.:
- Michigan State Univ., East Lansing, MI (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1962726
- Grant/Contract Number:
- SC0017887; SC0018083
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. C
- Additional Journal Information:
- Journal Volume: 104; Journal Issue: 4; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Nuclear forces; Nucleon-nucleon interactions; Ab initio calculations; Nuclear many-body theory; Renormalization group
Citation Formats
Zhu, B., Wirth, R., and Hergert, H. Singular value decomposition and similarity renormalization group evolution of nuclear interactions. United States: N. p., 2021.
Web. doi:10.1103/physrevc.104.044002.
Zhu, B., Wirth, R., & Hergert, H. Singular value decomposition and similarity renormalization group evolution of nuclear interactions. United States. https://doi.org/10.1103/physrevc.104.044002
Zhu, B., Wirth, R., and Hergert, H. Mon .
"Singular value decomposition and similarity renormalization group evolution of nuclear interactions". United States. https://doi.org/10.1103/physrevc.104.044002. https://www.osti.gov/servlets/purl/1962726.
@article{osti_1962726,
title = {Singular value decomposition and similarity renormalization group evolution of nuclear interactions},
author = {Zhu, B. and Wirth, R. and Hergert, H.},
abstractNote = {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.},
doi = {10.1103/physrevc.104.044002},
journal = {Physical Review. C},
number = 4,
volume = 104,
place = {United States},
year = {Mon Oct 11 00:00:00 EDT 2021},
month = {Mon Oct 11 00:00:00 EDT 2021}
}
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