中国物理B ›› 2025, Vol. 34 ›› Issue (2): 27504-027504.doi: 10.1088/1674-1056/ada758

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Auxiliary-field Monte Carlo method for frustrated spin systems

Ning Cai(蔡凝)1, Yuan Gao(高源)2,3, Wei Li(李伟)3,4,†, and Yang Qi(戚扬)1,‡   

  1. 1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China;
    2 School of Physics, Beihang University, Beijing 100191, China;
    3 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
    4 Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
  • 收稿日期:2024-12-05 修回日期:2024-12-05 接受日期:2025-01-08 出版日期:2025-02-15 发布日期:2025-01-15
  • 通讯作者: Wei Li, Yang Qi E-mail:w.li@itp.ac.cn;qiyang@fudan.edu.cn
  • 基金资助:
    W.L. acknowledges supports by the National Key Research and Development Program of China (Grant No. 2024YFA1409200), the National Natural Science Foundation of China (Grant Nos. 12222412 and 12047503), and CAS Project for Young Scientists in Basic Research (Grant No. YSBR-057). Y.Q. acknowledges supports by the National Natural Science Foundation of China (Grant No. 12374144).

Auxiliary-field Monte Carlo method for frustrated spin systems

Ning Cai(蔡凝)1, Yuan Gao(高源)2,3, Wei Li(李伟)3,4,†, and Yang Qi(戚扬)1,‡   

  1. 1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China;
    2 School of Physics, Beihang University, Beijing 100191, China;
    3 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
    4 Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
  • Received:2024-12-05 Revised:2024-12-05 Accepted:2025-01-08 Online:2025-02-15 Published:2025-01-15
  • Contact: Wei Li, Yang Qi E-mail:w.li@itp.ac.cn;qiyang@fudan.edu.cn
  • Supported by:
    W.L. acknowledges supports by the National Key Research and Development Program of China (Grant No. 2024YFA1409200), the National Natural Science Foundation of China (Grant Nos. 12222412 and 12047503), and CAS Project for Young Scientists in Basic Research (Grant No. YSBR-057). Y.Q. acknowledges supports by the National Natural Science Foundation of China (Grant No. 12374144).

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摘要： We extend a semiclassical numerical method, bosonic auxiliary-field Monte Carlo, to quantum spin systems. This method breaks the lattice into clusters, solves each cluster precisely and couples them with classical auxiliary fields through classical Monte Carlo simulation. We test the method with antiferromagnetic spin models in one-dimensional chains, square lattices and triangular lattices, and obtain reasonable results at finite temperatures. This algorithm builds a bridge between classical Monte Carlo method and quantum methods. The algorithm can be improved with either progress in classical Monte Carlo sampling or the development of quantum solvers, and can also be further applied to systems with different lattices or interactions.

关键词: Monte Carlo, quantum many-body system, frustrated magnets

Abstract: We extend a semiclassical numerical method, bosonic auxiliary-field Monte Carlo, to quantum spin systems. This method breaks the lattice into clusters, solves each cluster precisely and couples them with classical auxiliary fields through classical Monte Carlo simulation. We test the method with antiferromagnetic spin models in one-dimensional chains, square lattices and triangular lattices, and obtain reasonable results at finite temperatures. This algorithm builds a bridge between classical Monte Carlo method and quantum methods. The algorithm can be improved with either progress in classical Monte Carlo sampling or the development of quantum solvers, and can also be further applied to systems with different lattices or interactions.

Key words: Monte Carlo, quantum many-body system, frustrated magnets

中图分类号:  (Quantized spin models, including quantum spin frustration)

  • 75.10.Jm
87.55.K- (Monte Carlo methods)