中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10101-010101.doi: 10.1088/1674-1056/ae1c21

• •    下一篇

Practical algorithm for simulating thermal pure quantum states

Wei-Bo He(何伟博)1,2, Yun-Tong Yang(杨贇彤)1,2, and Hong-Gang Luo(罗洪刚)1,2,†   

  1. 1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
    2 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2025-09-03 修回日期:2025-10-21 接受日期:2025-11-06 发布日期:2025-12-29
  • 通讯作者: Hong-Gang Luo E-mail:luohg@lzu.edu.cn
  • 基金资助:
    The authors acknowledge Fu-Zhou Chen for helpful discussions. The work is partly supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402704) and the National Natural Science Foundation of China (Grant No. 12247101).

Practical algorithm for simulating thermal pure quantum states

Wei-Bo He(何伟博)1,2, Yun-Tong Yang(杨贇彤)1,2, and Hong-Gang Luo(罗洪刚)1,2,†   

  1. 1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
    2 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
  • Received:2025-09-03 Revised:2025-10-21 Accepted:2025-11-06 Published:2025-12-29
  • Contact: Hong-Gang Luo E-mail:luohg@lzu.edu.cn
  • Supported by:
    The authors acknowledge Fu-Zhou Chen for helpful discussions. The work is partly supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402704) and the National Natural Science Foundation of China (Grant No. 12247101).

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摘要： The development of novel quantum many-body computational algorithms relies on robust benchmarking. However, generating such benchmarks is often hindered by the massive computational resources required for exact diagonalization or quantum Monte Carlo simulations, particularly at finite temperatures. In this work, we propose a new algorithm for obtaining thermal pure quantum states, which allows efficient computation of both mechanical and thermodynamic properties at finite temperatures. We implement this algorithm in our open-source C++ template library, Physica. Combining the improved algorithm with state-of-the-art software engineering, our implementation achieves high performance and numerical stability. As an example, we demonstrate that for the $4 \times 4$ Hubbard model, our method runs approximately $10^3$ times faster than $\mathcal{H}\varPhi$ 3.5.2. Moreover, the accessible temperature range is extended down to $\beta = 32$ across arbitrary doping levels. These advances significantly push forward the frontiers of benchmarking for quantum many-body systems.

关键词: Physica, thermal pure quantum states, Hubbard model, strong correlated electron systems

Abstract: The development of novel quantum many-body computational algorithms relies on robust benchmarking. However, generating such benchmarks is often hindered by the massive computational resources required for exact diagonalization or quantum Monte Carlo simulations, particularly at finite temperatures. In this work, we propose a new algorithm for obtaining thermal pure quantum states, which allows efficient computation of both mechanical and thermodynamic properties at finite temperatures. We implement this algorithm in our open-source C++ template library, Physica. Combining the improved algorithm with state-of-the-art software engineering, our implementation achieves high performance and numerical stability. As an example, we demonstrate that for the $4 \times 4$ Hubbard model, our method runs approximately $10^3$ times faster than $\mathcal{H}\varPhi$ 3.5.2. Moreover, the accessible temperature range is extended down to $\beta = 32$ across arbitrary doping levels. These advances significantly push forward the frontiers of benchmarking for quantum many-body systems.

Key words: Physica, thermal pure quantum states, Hubbard model, strong correlated electron systems

中图分类号:  (Computer software and software reviews)

  • 01.50.hv
02.70.-c (Computational techniques; simulations) 05.30.-d (Quantum statistical mechanics) 71.10.-w (Theories and models of many-electron systems)