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Title: Factorization in large-scale many-body calculations

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 Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.
 [1] ;  [2] ;  [3]
  1. San Diego State Univ., San Diego, CA (United States). Dept. of Physics
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. 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:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0010-4655
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 184; Journal Issue: 12; Journal ID: ISSN 0010-4655
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; shell model; configuration interaction; many-body