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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
+ Show Author Affiliations

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 Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-76SF00515; AC02-05CH11231
OSTI ID:
1423515
Alternate ID(s):
OSTI ID: 1564396
Journal Information:
Computer Physics Communications, Journal Name: Computer Physics Communications Journal Issue: C Vol. 224; ISSN 0010-4655
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (4)

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
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
Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots text January 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Checkerboard decomposition
Exact diagonalization
Hubbard model
Many-body physics
Perfect hashing
Strongly correlated system