Paradeisos: A perfect hashing algorithm for manybody eigenvalue problems
Abstract
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 manybody Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of singleparticle basis states for each element in the manybody 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 manybody, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic singleband Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.
 Authors:

 SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
 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
 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
 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:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1423515
 Alternate Identifier(s):
 OSTI ID: 1564396
 Grant/Contract Number:
 AC0276SF00515; AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Manybody physics; Strongly correlated system; Perfect hashing; Exact diagonalization; Hubbard model; Checkerboard decomposition
Citation Formats
Jia, C. J., Wang, Y., Mendl, C. B., Moritz, B., and Devereaux, T. P. Paradeisos: A perfect hashing algorithm for manybody eigenvalue problems. United States: N. p., 2017.
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 manybody 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. Sat .
"Paradeisos: A perfect hashing algorithm for manybody eigenvalue problems". United States. doi:10.1016/j.cpc.2017.11.011. https://www.osti.gov/servlets/purl/1423515.
@article{osti_1423515,
title = {Paradeisos: A perfect hashing algorithm for manybody 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 manybody Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of singleparticle basis states for each element in the manybody 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 manybody, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic singleband 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}
}
Web of Science