High Performance Computing for Eigenvalue Solver in Density-Matrix Renormalization Group Method: Parallelization of the Hamiltonian Matrix-Vector Multiplication

Authors:
Susumu Yamada;Masahiko Okumura;Masahiko Machida
Affiliations:
CCSE, Japan Atomic Energy Agency, Tokyo, Japan 110-0015 and CREST(JST), Kawaguchi, Japan 330-0012;CCSE, Japan Atomic Energy Agency, Tokyo, Japan 110-0015 and CREST(JST), Kawaguchi, Japan 330-0012;CCSE, Japan Atomic Energy Agency, Tokyo, Japan 110-0015 and CREST(JST), Kawaguchi, Japan 330-0012
Venue:
High Performance Computing for Computational Science - VECPAR 2008
Year:
2008

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Abstract

The Density Matrix Renormalization Group (DMRG) method is widely used by computational physicists as a high accuracy tool to obtain the ground state of large quantum lattice models. Since the DMRG method has been originally developed for 1-D models, many extended method to a 2-D model have been proposed. However, some of them have issues in term of their accuracy. It is expected that the accuracy of the DMRG method extended directly to 2-D models is excellent. The direct extension DMRG method demands an enormous memory space. Therefore, we parallelize the matrix-vector multiplication in iterative methods for solving the eigenvalue problem, which is the most time- and memory-consuming operation. We find that the parallel efficiency of the direct extension DMRG method shows a good one as the number of states kept increases.