Factorization in largescale manybody calculations
Abstract
One approach for solving interacting manyfermion systems is the configurationinteraction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a manybody basis of Slater determinants (antisymmetrized products of singleparticle 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 manybody 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 ‘doublefactorization’ which speeds up basis generation and setup of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configurationinteraction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.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 Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1305899
 Report Number(s):
 LLNLJRNL624065
Journal ID: ISSN 00104655
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 184; Journal Issue: 12; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; shell model; configuration interaction; manybody
Citation Formats
Johnson, Calvin W., Ormand, W. Erich, and Krastev, Plamen G. Factorization in largescale manybody 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 largescale manybody calculations. United States. doi:10.1016/j.cpc.2013.07.022.
Johnson, Calvin W., Ormand, W. Erich, and Krastev, Plamen G. Wed .
"Factorization in largescale manybody calculations". United States. doi:10.1016/j.cpc.2013.07.022. https://www.osti.gov/servlets/purl/1305899.
@article{osti_1305899,
title = {Factorization in largescale manybody calculations},
author = {Johnson, Calvin W. and Ormand, W. Erich and Krastev, Plamen G.},
abstractNote = {One approach for solving interacting manyfermion systems is the configurationinteraction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a manybody basis of Slater determinants (antisymmetrized products of singleparticle 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 manybody 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 ‘doublefactorization’ which speeds up basis generation and setup of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configurationinteraction 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 = {2013},
month = {8}
}
Web of Science