Factorization in large-scale many-body calculations
Abstract
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 Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.
- Authors:
-
- 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
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1305899
- Report Number(s):
- LLNL-JRNL-624065
Journal ID: ISSN 0010-4655
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Physics Communications
- Additional Journal Information:
- Journal Volume: 184; Journal Issue: 12; Journal ID: ISSN 0010-4655
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; shell model; configuration interaction; many-body
Citation Formats
Johnson, Calvin W., Ormand, W. Erich, and Krastev, Plamen G. Factorization in large-scale many-body calculations. United States: N. p., 2013.
Web. doi:10.1016/j.cpc.2013.07.022.
Johnson, Calvin W., Ormand, W. Erich, & Krastev, Plamen G. Factorization in large-scale many-body calculations. United States. https://doi.org/10.1016/j.cpc.2013.07.022
Johnson, Calvin W., Ormand, W. Erich, and Krastev, Plamen G. Wed .
"Factorization in large-scale many-body calculations". United States. https://doi.org/10.1016/j.cpc.2013.07.022. https://www.osti.gov/servlets/purl/1305899.
@article{osti_1305899,
title = {Factorization in large-scale many-body calculations},
author = {Johnson, Calvin W. and Ormand, W. Erich and Krastev, Plamen G.},
abstractNote = {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.},
doi = {10.1016/j.cpc.2013.07.022},
journal = {Computer Physics Communications},
number = 12,
volume = 184,
place = {United States},
year = {Wed Aug 07 00:00:00 EDT 2013},
month = {Wed Aug 07 00:00:00 EDT 2013}
}
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Accelerating many-nucleon basis generation for high performance computing enabled ab initio nuclear structure studies
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Inelastic nuclear scattering from neutrinos and dark matter
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Large-scale exact diagonalizations reveal low-momentum scales of nuclei
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