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| Abstract: |
| The analytic continuation serves as a crucial bridge between quantum Monte Carlo calculations in imaginary-time formalism—specifically, the Green"s functions—and physical measurements (the spectral functions) in real time. Various approaches have been developed to enhance the accuracy of analytic continuation, including the Padé approximation, the maximum entropy method, and stochastic analytic continuation. In this work, we employ different deep learning techniques to investigate the analytic continuation for the quantum impurity model. A significant challenge in this context is that the sharp Abrikosov-Suhl resonance peak may be either underestimated or overestimated. We fit both the imaginary-time Green"s function and the spectral function using Chebyshev polynomials in logarithmic coordinates. We utilize full-connected networks, convolutional neural networks, and residual networks to address this issue. Our findings indicate that introducing noise during the training phase significantly improves the accuracy of the learning process. The typical absolute error achieved is less than 10-4 orders. These investigations pave the way for machine learning to optimize the analytic continuation problem in many-body systems, thereby reducing the need for prior expertise in physics. |
| Key words: machine learning analytic continuation neural networks |
| DOI：10.11916/j.issn.1005-9113.24027 |
| Clc Number:Grant No. 12174101 |
| Fund: |
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| Descriptions in Chinese: |
| 解析延拓是虚时间形式的量子蒙特卡罗计算(格林函数)和实时物理测量(谱函数)之间的重要桥梁。改进解析延拓的方法有:Padé近似法、最大熵法和随机解析延拓。在这项工作中，我们使用不同的深度学习方法来研究量子杂质模型的解析延拓。这个问题的一个关键难题是尖锐的Abrikosov-Suhl共振峰能否被准确评估。本文采用对数坐标下的切比雪夫多项式拟合虚时格林函数和谱函数，利用全连通网络、卷积神经网络和残差网络进行求解。我们发现在训练阶段引入噪声显著改善了学习过程。获得的典型绝对误差小于0.0001。这些研究为机器学习优化多体系统中的解析延拓问题铺平了道路，消除了对物理专业知识的需求。 |
