Neural network analytic continuation for Monte Carlo: Improvement by statistical errors

doi:10.1088/1674-1056/accd4c

中国物理B ›› 2023, Vol. 32 ›› Issue (7): 70705-070705.doi: 10.1088/1674-1056/accd4c

Neural network analytic continuation for Monte Carlo: Improvement by statistical errors

Kai-Wei Sun(孙恺伟)¹ and Fa Wang(王垡)^1,2,†

1 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China;
2 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

收稿日期:2023-02-17 修回日期:2023-04-13 接受日期:2023-04-16 出版日期:2023-06-15 发布日期:2023-06-21
通讯作者: Fa Wang E-mail:wangfa@pku.edu.cn
基金资助:
FW acknowledges support from the National Natural Science Foundation of China (Grant Nos. 12274004 and 11888101). Quantum Monte Carlo simulations are performed on TianHe-1A of National Supercomputer Center in Tianjin.

Neural network analytic continuation for Monte Carlo: Improvement by statistical errors

Kai-Wei Sun(孙恺伟)¹ and Fa Wang(王垡)^1,2,†

1 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China;
2 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

Received:2023-02-17 Revised:2023-04-13 Accepted:2023-04-16 Online:2023-06-15 Published:2023-06-21
Contact: Fa Wang E-mail:wangfa@pku.edu.cn
Supported by:
FW acknowledges support from the National Natural Science Foundation of China (Grant Nos. 12274004 and 11888101). Quantum Monte Carlo simulations are performed on TianHe-1A of National Supercomputer Center in Tianjin.

摘要/Abstract

摘要： This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are carefully synthesized without "data leakage". We find that the training set should match the input correlation functions in terms of statistical error properties, such as noise level, noise dependence on imaginary time, and imaginary time-displaced correlations. We have developed a systematic method to synthesize such training datasets. Our improved algorithm outperforms the widely used maximum entropy method in highly noisy situations. As an example, our method successfully extracted the dynamic structure factor of the spin-1/2 Heisenberg chain from quantum Monte Carlo simulations.

关键词: neural network, analytic continuation, quantum Monte Carlo

Abstract: This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are carefully synthesized without "data leakage". We find that the training set should match the input correlation functions in terms of statistical error properties, such as noise level, noise dependence on imaginary time, and imaginary time-displaced correlations. We have developed a systematic method to synthesize such training datasets. Our improved algorithm outperforms the widely used maximum entropy method in highly noisy situations. As an example, our method successfully extracted the dynamic structure factor of the spin-1/2 Heisenberg chain from quantum Monte Carlo simulations.

Key words: neural network, analytic continuation, quantum Monte Carlo

中图分类号: (Neural networks, fuzzy logic, artificial intelligence)

07.05.Mh

02.70.Ss (Quantum Monte Carlo methods)

Kai-Wei Sun(孙恺伟) and Fa Wang(王垡). Neural network analytic continuation for Monte Carlo: Improvement by statistical errors[J]. 中国物理B, 2023, 32(7): 70705-070705.

Kai-Wei Sun(孙恺伟) and Fa Wang(王垡). Neural network analytic continuation for Monte Carlo: Improvement by statistical errors[J]. Chin. Phys. B, 2023, 32(7): 70705-070705.

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Neural network analytic continuation for Monte Carlo: Improvement by statistical errors

Neural network analytic continuation for Monte Carlo: Improvement by statistical errors

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