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

Journal Article · · Computer Physics Communications
 [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
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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.

Research Organization:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
AC02-76SF00515; AC02-05CH11231
OSTI ID:
1423515
Alternate ID(s):
OSTI ID: 1564396
Journal Information:
Computer Physics Communications, Vol. 224, Issue C; ISSN 0010-4655
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

References (14)

Computational Studies of Quantum Spin Systems
  • 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 https://doi.org/10.1063/1.3518900
conference January 2010
Correlated electrons in high-temperature superconductors journal July 1994
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
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
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

Cited By (4)

A Scalable Matrix-Free Iterative Eigensolver for Studying Many-Body Localization
  • Van Beeumen, Roel; Kahanamoku-Meyer, Gregory D.; Yao, Norman Y.
  • HPCAsia2020: International Conference on High Performance Computing in Asia-Pacific Region, Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region https://doi.org/10.1145/3368474.3368497
conference January 2020
Theoretical understanding of photon spectroscopies in correlated materials in and out of equilibrium journal August 2018
Ab initio exact diagonalization simulation of the Nagaoka transition in quantum dots journal October 2019
Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots text January 2019

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Related Subjects

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