Analysis of pseudo-random number generators in QMC-SSE method

doi:10.1088/1674-1056/ad1e69

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 37509-037509.doi: 10.1088/1674-1056/ad1e69

Analysis of pseudo-random number generators in QMC-SSE method

Dong-Xu Liu(刘东旭), Wei Xu(徐维), and Xue-Feng Zhang(张学锋)^†

Department of Physics, Chongqing University, Chongqing 401331, China

收稿日期:2023-11-13 修回日期:2024-01-09 接受日期:2024-01-15 出版日期:2024-02-22 发布日期:2024-02-29
通讯作者: Xue-Feng Zhang E-mail:zhangxf@cqu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12274046, 11874094, and 12147102), Chongqing Natural Science Foundation (Grant No. CSTB2022NSCQ-JQX0018), and Fundamental Research Funds for the Central Universities (Grant No. 2021CDJZYJH- 003).

Analysis of pseudo-random number generators in QMC-SSE method

Dong-Xu Liu(刘东旭), Wei Xu(徐维), and Xue-Feng Zhang(张学锋)^†

Department of Physics, Chongqing University, Chongqing 401331, China

Received:2023-11-13 Revised:2024-01-09 Accepted:2024-01-15 Online:2024-02-22 Published:2024-02-29
Contact: Xue-Feng Zhang E-mail:zhangxf@cqu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12274046, 11874094, and 12147102), Chongqing Natural Science Foundation (Grant No. CSTB2022NSCQ-JQX0018), and Fundamental Research Funds for the Central Universities (Grant No. 2021CDJZYJH- 003).

摘要/Abstract

摘要： In the quantum Monte Carlo (QMC) method, the pseudo-random number generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process. Here, we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion (SSE) algorithm. To quantitatively compare them, we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms. After testing several representative observables of the Heisenberg model in one and two dimensions, we recommend the linear congruential generator as the best choice of PRNG. Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.

关键词: stochastic series expansion, quantum Monte Carlo, pseudo-random number generator

Abstract: In the quantum Monte Carlo (QMC) method, the pseudo-random number generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process. Here, we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion (SSE) algorithm. To quantitatively compare them, we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms. After testing several representative observables of the Heisenberg model in one and two dimensions, we recommend the linear congruential generator as the best choice of PRNG. Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.

Key words: stochastic series expansion, quantum Monte Carlo, pseudo-random number generator

中图分类号: (Numerical simulation studies)

75.40.Mg

02.70.Ss (Quantum Monte Carlo methods) 75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.))

Dong-Xu Liu(刘东旭), Wei Xu(徐维), and Xue-Feng Zhang(张学锋). Analysis of pseudo-random number generators in QMC-SSE method[J]. 中国物理B, 2024, 33(3): 37509-037509.

Dong-Xu Liu(刘东旭), Wei Xu(徐维), and Xue-Feng Zhang(张学锋). Analysis of pseudo-random number generators in QMC-SSE method[J]. Chin. Phys. B, 2024, 33(3): 37509-037509.

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Analysis of pseudo-random number generators in QMC-SSE method

Analysis of pseudo-random number generators in QMC-SSE method

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