ACM/IEEE SC 2005 Conference (SC'05)
DOI: 10.1109/sc.2005.1
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16.447 TFlops and 159-Billion-dimensional Exact-diagonalization for Trapped Fermion-Hubbard Model on the Earth Simulator

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Cited by 24 publications
(32 citation statements)
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“…This partition of the vector space leads to a more simplified partition of the operator than eq. (B·2), H ¼ H "" 1 þ 1 H ## þ ðresidual partÞ, 13) where H "" and H ## include the hopping terms and part of the on-site Coulomb interaction. As a result, the memory required to store the Hamiltonian reduced to 1 GB.…”
Section: Discussion and Summarymentioning
confidence: 99%
“…This partition of the vector space leads to a more simplified partition of the operator than eq. (B·2), H ¼ H "" 1 þ 1 H ## þ ðresidual partÞ, 13) where H "" and H ## include the hopping terms and part of the on-site Coulomb interaction. As a result, the memory required to store the Hamiltonian reduced to 1 GB.…”
Section: Discussion and Summarymentioning
confidence: 99%
“…Although the dimension partly decreases by eliminating clear irrelevant states, the calculation solving the ground state of the superblock Hamiltonian matrix is obviously the most time-and memory-consuming. Since the Hamiltonian matrix is a sparse symmetric matrix, an iterative method, such as Lanczos method [1] or conjugate gradient method [5,6,19,20], is suitable for solving the ground state. Inside these iterative calculation steps, the heaviest operation is a multiplication of the superblock Hamiltonian matrix and a vector.…”
Section: Algorithmmentioning
confidence: 99%
“…Among them, the most accurate one is the so-called "exact diagonalization method", which solves the ground state of the model Hamiltonian matrix. It is mathematically equivalent to calculating an eigenvector whose eigenvalue is the lowest for a symmetric Hamiltonian matrix (see, e.g., [19,20] for the parallelization of the exact diagonalization and [7][8][9] for the calculation results). However, since the Hamiltonian matrix size increases almost exponentially with the system size, i.e., the numbers of electrons and lattice sites, the truncation of irrelevant states has been an important issue in this research field.…”
Section: Introductionmentioning
confidence: 99%
“…The most accurate one of them is the exact diagonalization method, which solves the ground state (the smallest eigenvalue and the corresponding eigenvector) of the Hamiltonian matrix derived from the systems. We have actually parallelized the exact diagonalization method and obtained some novel physical results [4][5][6][7]. However, the dimension of the Hamiltonian matrix for the exact diagonalization method increases almost exponentially with the number of the lattice sites.…”
Section: Introductionmentioning
confidence: 99%
“…However, the dimension of the Hamiltonian matrix for the exact diagonalization method increases almost exponentially with the number of the lattice sites. Thus, the limit of the simulation on a supercomputer with a terabyte memory system is an about-20-site system [6,7].…”
Section: Introductionmentioning
confidence: 99%