Parallel computing of directly-extended density-matrix renormalization group to two-dimensional strongly correlated quantum systems

Yamada, Susumu  ; Okumura, Masahiko   ; Machida, Masahiko  

The Density Matrix Renormalization Group (DMRG) method is widely used by computational physicists as a high accuracy tool to explore the ground state of large quantum lattice systems. However, the reliable results by DMRG are limited only for 1-D or two-leg ladder models in spite of a great demand for 2-D system. The reason is that the direct extension to 2-D requires an enormous memory space while the technical extension based on 1-D algorithm does not keep the accuracy in 1-D systems. Therefore, we parallelize the direct 2-D DMRG code on a large-scale supercomputer and examine the accuracy and the performance for typical lattice models, i.e., Heisenberg and Hubbard models. The parallelization is mainly made on the multiplication of the Hamiltonian matrix and vectors. We find that the parallelization efficiency, i.e., the speed up ratio with increasing the number of CPU, shows a good one as the number of states kept increases. This result is promising for future 2-D parallel DMRG simulations.