Application of the cluster nonequilibrium relenaxation method to quantum Monte Carlo calculations

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05493
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: National Institute for Materials Science
• Principal Investigator: NONOMURA yoshihiko 国立研究開発法人物質・材料研究機構, 国際ナノアーキテクトニクス研究拠点, 主幹研究員 (30280936)
• Co-Investigator(Kenkyū-buntansha): 富田 裕介 芝浦工業大学, 工学部, 教授 (50361663)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 計算物理学 / 数理物理学 / 量子モンテカルロ法 / 非平衡緩和法 / クラスターアルゴリズム / スケーリング理論

Outline of Final Research Achievements

We generalized the cluster nonequilibrium relaxation method to the standard quantum Monte Carlo scheme, namely the continuous-time loop algorithm, and investigated the Neel-dimer quantum phase transition in the two-dimensional dimerized S=1/2 antiferromagnetic Heisenberg model. With the scaling analysis based on the stretched-exponential ordering from the isolated dimer state, we estimated the quantum critical point and critical exponents accurately. In order to establish the theoretical basis of the present scheme, we obtained the exact solution of the nonequilibrium relaxation process in the infinite-range Ising model based on the Swendsen-Wang cluster algorithm, and derived the stretched-exponential relaxation formula phenomenologically based on a dynamical relation settled in this exact solution. Furthermore, we generalized the “temperature scaling”, which scales off-critical data during nonequilibrium relaxation in local-update algorithms, to that in cluster-update algorithms.

Free Research Field

物性基礎理論・計算物理学

Academic Significance and Societal Importance of the Research Achievements

量子ゆらぎで相転移が起こる系は、空間次元に加えて仮想的な次元も導入しないと数値計算ができないため、扱える系の大きさに厳しい制約があり、効率的な計算手法の開発が望まれてきた。本研究で提案した手法は、緩和が極端に遅い系や、不純物のさまざまな分布を平均しないと振舞がわからない系など、従来の計算手法では絶望的だと思われてきた状況になるほど強みを発揮する。