Generalization of cluster nonequilibrium relaxation method to off-critical region and its applications

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K03777
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• 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): 2020-04-01 – 2023-03-31
• Keywords: 温度スケーリング / 非平衡緩和法 / クラスターアルゴリズム / 量子相転移 / 希釈系

Outline of Final Research Achievements

In Monte Carlo study of phase transitions in spin systems, information of critical phenomena can be derived merely from initial-time relaxations. Such a Monte Carlo scheme to skip equilibration is called as the nonequilibrium relaxation method. In conventional local-update algorithms, such a scheme was formulated both for critical and off-critical cases, while in cluster-update algorithms, it had been formulated only for critical cases. In the present study we proposed such a scheme for off-critical cases, called as the temperature scaling. This scheme was confirmed in the magnetic phase transition in the 3D classical Heisenberg model and in the Neel-dimer quantum phase transition in the 2D quantum antiferromagnetic Heisenberg model. Coupled with the nonequilibrium-to-equilibrium scaling at the critical point, all the critical exponents can be evaluated efficiently. Especially in quantum spin systems, time-consuming calculations on off-diagonal quantities are not necessary anymore.

Free Research Field

物性基礎理論

Academic Significance and Societal Importance of the Research Achievements

モンテカルロ法による相転移の研究は幅広い応用の可能性があり、効率的な計算手法の開発は意義深い。我々は、本来は長時間緩和を要する平衡状態の情報を緩和初期の振舞から得る手法を研究してきた。大域的な状態更新で緩和を加速したアルゴリズムにもこの手法が使えることを我々は示したが、本研究で転移点から外れた緩和データからも情報が得られるようになり、さらに効率化が進んだ。特に本研究の手法を量子系に適用すると、従来手法では量子効果を直接扱うことになり多大なコストを要していた計算が回避されるので非常に効率的である。