量子多体系・高精度シミュレーションの研究開発; 密度行列繰り込み群法の超並列化と大規模計算

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

山田 進  ; 五十嵐 亮; 奥村 雅彦*   ; 今村 俊幸*; 町田 昌彦  

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

本論文は、CREST及び科学研究費補助金の研究計画に従い、量子多体系のシミュレーション手法である密度行列繰り込み群(DMRG)法の並列化に関する研究成果の発表である。特筆すべき成果は、超並列計算機を想定し、問題の物理的性質を考慮した並列化手法を提案した点にあり、実際に東京大学のT2Kクラスタシステムを利用したシミュレーションにより1000を超えるコア数でも並列化の効果が得られることを確認した。この結果から、本成果は次世代計算機のような超並列計算機の性能を有効に利用するための、重要な1つの並列化の指針になることが期待される。

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.