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Title: Paradeisos: A perfect hashing algorithm for many-body 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 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:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1423515
Alternate Identifier(s):
OSTI ID: 1564396
Grant/Contract Number:  
AC02-76SF00515; AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
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

Citation Formats

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., 2017. Web. https://doi.org/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. https://doi.org/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 many-body eigenvalue problems". United States. https://doi.org/10.1016/j.cpc.2017.11.011. https://www.osti.gov/servlets/purl/1423515.
@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}
}

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Cited by: 4 works
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Works referenced in this record:

Computational Studies of Quantum Spin Systems
conference, January 2010

  • Sandvik, Anders W.; Avella, Adolfo; Mancini, Ferdinando
  • LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XIV: Fourteenth Training Course in the Physics of Strongly Correlated Systems, AIP Conference Proceedings
  • DOI: 10.1063/1.3518900

Correlated electrons in high-temperature superconductors
journal, July 1994


Ground-state energy and spin gap of spin- 1 2 Kagomé-Heisenberg antiferromagnetic clusters: Large-scale exact diagonalization results
journal, June 2011


Static and dynamical properties of doped Hubbard clusters
journal, May 1992


Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
journal, January 2017


Exact Diagonalization of Heisenberg SU ( N ) Models
journal, September 2014


Exact diagonalization: the Bose–Hubbard model as an example
journal, April 2010


Exact diagonalization of quantum-spin models
journal, October 1990


Theory of Two-Magnon Raman Scattering in Iron Pnictides and Chalcogenides
journal, February 2011


Momentum Dependence of Resonant Inelastic X-Ray Scattering Spectrum in Insulating Cuprates
journal, November 1999


Sitewise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators
journal, February 2015


Real-Space Visualization of Remnant Mott Gap and Magnon Excitations
journal, April 2014


Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
journal, March 1992

  • van der Vorst, H. A.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 13, Issue 2
  • DOI: 10.1137/0913035

A perfect Hashing function for exact diagonalization of many-body systems of identical particles
journal, November 1995


The FermiFab toolbox for fermionic many-particle quantum systems
journal, June 2011


Electron correlations in the two-dimensional Hubbard model: A group-theoretical and numerical study
journal, July 1992


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