High performance computing of density matrix renormalization group method for 2-dimensional model. Parallelization strategy toward peta computing

We parallelize the density matrix renormalization group (DMRG) method, which is a ground-state solver for one-dimensional quantum lattice systems. The parallelization allows us to extend the applicable range of the DMRG to n-leg ladders i.e., quasi two-dimension cases. Such an extension is regarded to bring about several breakthroughs in e.g., quantum-physics, chemistry, and nano-engineering. However, the straightforward parallelization requires all-to-all communications between all processes which are unsuitable for multi-core systems, which is a mainstream of current parallel computers. Therefore, we optimize the all-to-all communications by the following two steps. The first one is the elimination of the communications between all processes by only rearranging data distribution with the communication data amount kept. The second one is the avoidance of the communication conflict by rescheduling the calculation and the communication. We evaluate the performance of the DMRG method on multi-core supercomputers and confirm that our two-steps tuning is quite effective. (author)