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Title: Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems

Here, we describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the “checkerboard” decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.
Authors:
 [1] ;  [2] ;  [1] ;  [3] ;  [4]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES); Stanford Univ., CA (United States). Dept. of Applied Physics
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES); Univ. of North Dakota, Grand Forks, ND (United States). Dept. of Physics and Astrophysics
  4. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES); Stanford Univ., CA (United States). Geballe Lab. for Advanced Materials
Publication Date:
Grant/Contract Number:
AC02-76SF00515; AC02-05CH11231
Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Many-body physics; Strongly correlated system; Perfect hashing; Exact diagonalization; Hubbard model; Checkerboard decomposition
OSTI Identifier:
1423515

Jia, C. J., Wang, Y., Mendl, C. B., Moritz, B., and Devereaux, T. P.. Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems. United States: N. p., Web. doi:10.1016/j.cpc.2017.11.011.
Jia, C. J., Wang, Y., Mendl, C. B., Moritz, B., & Devereaux, T. P.. Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems. United States. doi:10.1016/j.cpc.2017.11.011.
Jia, C. J., Wang, Y., Mendl, C. B., Moritz, B., and Devereaux, T. P.. 2017. "Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems". United States. doi:10.1016/j.cpc.2017.11.011.
@article{osti_1423515,
title = {Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems},
author = {Jia, C. J. and Wang, Y. and Mendl, C. B. and Moritz, B. and Devereaux, T. P.},
abstractNote = {Here, we describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the “checkerboard” decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.},
doi = {10.1016/j.cpc.2017.11.011},
journal = {Computer Physics Communications},
number = C,
volume = 224,
place = {United States},
year = {2017},
month = {12}
}