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

• Published in: High Performance Computing for Computational Science - VECPAR 2008 pp. 39 - 45
• Main Authors: Yamada, Susumu, Okumura, Masahiko, Machida, Masahiko
• Format: Book Chapter
• Language: English; Japanese
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2008
• Series: Lecture Notes in Computer Science
• Subjects: DMRG method; eigenvalue problem; matrix-vector multiplication; Parallel and distributed computing; quantum lattice systems
• ISBN: 3540928588; 9783540928584
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-92859-1_5

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.