Research and development of highly-accurate simulation for quantum many-body systems; Parallel-computing of density matrix renormalization group method and ultra large-scale simulations

Yamada, Susumu  ; Igarashi, Ryo; Okumura, Masahiko*   ; Imamura, Toshiyuki*; Machida, Masahiko  

The density matrix renormalization group (DMRG) method is a numerical calculation technique to obtain the ground state of quantum lattice systems whose degree of freedoms exponentially grows with the size of the lattice sites and particles (or spins in interacting spin systems). Its advantage is excellent accuracy comparable to the exact diagonalization scheme even in considerably large number of sites and particles (spins). However, the technique has been originally developed for one-dimensional systems. Therefore, the extension to higher dimensional lattices systems is in great demand since major rich physics such as superconductivity and ferromagnetism frequently occurs in two or three dimensions. This paper describes a parallelization strategy of the technique to calculate quasi-two dimensional (ladder) systems toward the next generation supercomputer and reports its good parallel efficiency on T2K supercomputer HA8000 at University of Tokyo. Moreover, typical quantum phenomena obtained by using the parallelized code are exhibited and some remarks on parallelization scheme in the next generation supercomputer are mentioned.