2007 Fiscal Year Final Research Report Summary
Development of Numerical Algorithm for Quantum Atomic Gas
| Project/Area Number |
18500033
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Software
|
|---|
| Research Institution | Japan Atomic Energy Agency |
|---|
Principal Investigator |
SUSUMU Yamada Japan Atomic Energy Agency, Center for Computational Science & e-Systems, Scientist (80360436)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MACHIDA Masahiko Japan Atomic Energy Agency, システム計算科学センター, Principal Researcher (60360434)
OHASHI Yoji Keio University, Faculty of Science and Technology, Associate professor (60272134)
IMAMURA Toshiyuki The University of Electro-Communications, Department of Computer Science, Associate professor (60361838)
|
|---|
| Project Period (FY) |
2006 – 2007
|
| Keywords | High Performance Comnuting / Density Matrix Renormalization Group / The Earth Simulator / Eigenvalue Solver / Parallel Comnuting / Fermion / Hubbard model |
|---|
| Research Abstract |
In 2006, our research group developed a novel preconditioner for the conjugate gradient method in solving the ground state of the Hamiltonian matrix of the Hubbard model describing quantum atomic gases loaded on optical lattices. We proposed a preconditioner using an approximate eigenvalue obtained at each iteration step. The preconditioner improves the convergence property of the CG method by several times than that without the preconditioner. This research result was published in the transactions of the Japan Society for Computational Engineering and Science and selected as one of the outstanding paper award of JSCES.
In 2007, we focused on the Density Matrix Renormalization Group (DMRG) method, which is widely used by computational physicists as a high accuracy tool to obtain the ground state of large quantum lattice systems. It is well known that the DMRG method for 2-D models demands an enormous memory space. Therefore, we proposed a parallel algorithm of the DMRG, whose core is the parallelization of the matrix-vector multiplication repeated in solving the eigenvalue problem. Since the parallelization is made on the most time- and memory-consuming operation, the parallel DMRG method shows good parallel efficiency. We presented the results at the TASTED International Multi-Conference on Parallel and Distributed computing and Networks. Moreover, we examined 2-D Hubbard models systematically using our parallel DMRG method on SGI Altix 3700Bx2 in Japan Atomic Energy Agency, and published the physical insights obtained by this simulation in journals of physical field. (Phys. Rev. A)
|
