Communication strategy of parallel density-matrix renormalization group method with considering architecture of multi-core cluster

Yamada, Susumu  ; Imamura, Toshiyuki*; Machida, Masahiko  

We parallelize the density matrix renormalization group (DMRG) method, which is a groundstate solver for one-dimensional quantum lattice systems. The parallelization allows us to extend the applicable range of the DMRG to multiple leg ladders or quasi two-dimension cases. Such an extension is regarded to bring about several breakthroughs in quantum physics, chemistry, nano-device engineering, and so on. The parallelization requires an all-to-all communication which involves all processes. Such a communication is not suitable for multi-core clusters, which are presently the main stream of the parallel computer, because the network bandwidth should be shared by a large number of processes. Therefore, we propose a new communication strategy to eliminate the all-to-all communication by rearranging a data distribution. We evaluate performance of the new strategy on "SGI Altix 3700Bx2" (single-core system) and "T2K Open Supercomputer (Todai Combined Cluster)" (quad-core system) and confirm that the strategy is quite crucial for typical multi-core systems like T2K.