Factorization in large-scale many-body calculations

Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.

doi:10.1016/j.cpc.2013.07.022

Title: Factorization in large-scale many-body calculations

Journal Article · Wed Aug 07 00:00:00 EDT 2013 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2013.07.022· OSTI ID:1305899

Johnson, Calvin W. ^[1]; Ormand, W. Erich ^[2]; Krastev, Plamen G. ^[3]

San Diego State Univ., San Diego, CA (United States). Dept. of Physics
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
San Diego State Univ., San Diego, CA (United States). Dept. of Physics; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Harvard Univ., Cambridge, MA (United States). Research Computing, Faculty of Arts and Sciences

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elements on the fly and can reduce the storage requirements by an order of magnitude or more. Here, we discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1305899

Report Number(s):: LLNL-JRNL-624065

Journal Information:: Computer Physics Communications, Vol. 184, Issue 12; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 58 works

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Cited By (6)

Monte Carlo shell model studies with massively parallel supercomputers Shimizu, Noritaka; Abe, Takashi; Honma, Michio Physica Scripta, Vol. 92, Issue 6 https://doi.org/10.1088/1402-4896/aa65e4	journal	April 2017
Accelerating many-nucleon basis generation for high performance computing enabled ab initio nuclear structure studies Langr, Daniel; Dytrych, Tomáš; Launey, Kristina D. The International Journal of High Performance Computing Applications, Vol. 33, Issue 3 https://doi.org/10.1177/1094342019838314	journal	March 2019
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Inelastic nuclear scattering from neutrinos and dark matter Dutta, Bhaskar; Huang, Wei-Chih; Newstead, Jayden L. Physical Review D, Vol. 106, Issue 11 https://doi.org/10.1103/physrevd.106.113006	journal	December 2022
Large-scale exact diagonalizations reveal low-momentum scales of nuclei Forssén, C.; Carlsson, B. D.; Johansson, H. T. arXiv https://doi.org/10.48550/arxiv.1712.09951	text	January 2017
Toward Scalable Many-Body Calculations for Nuclear Open Quantum Systems using the Gamow Shell Model Michel, Nicolas; Aktulga, Hasan Metin; Jaganathen, Yannen arXiv https://doi.org/10.48550/arxiv.1911.06494	text	January 2019

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