Prediction of impurity spectrum function by deep learning algorithm

doi:10.1088/1674-1056/ad3908

中国物理B ›› 2024, Vol. 33 ›› Issue (5): 57102-057102.doi: 10.1088/1674-1056/ad3908

Prediction of impurity spectrum function by deep learning algorithm

Ting Liu(刘婷)¹, Rong-Sheng Han(韩榕生)^1,2,3, and Liang Chen(陈亮)^1,2,3,†

1 School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
2 Institute of Condensed Matter Physics, North China Electric Power University, Beijing 102206, China;
3 Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China

收稿日期:2023-12-01 修回日期:2024-03-09 接受日期:2024-03-29 出版日期:2024-05-20 发布日期:2024-05-20
通讯作者: Liang Chen E-mail:slchern@ncepu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12174101) and the Fundamental Research Funds for the Central Universities (Grant No. 2022MS051).

Prediction of impurity spectrum function by deep learning algorithm

Ting Liu(刘婷)¹, Rong-Sheng Han(韩榕生)^1,2,3, and Liang Chen(陈亮)^1,2,3,†

1 School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
2 Institute of Condensed Matter Physics, North China Electric Power University, Beijing 102206, China;
3 Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China

Received:2023-12-01 Revised:2024-03-09 Accepted:2024-03-29 Online:2024-05-20 Published:2024-05-20
Contact: Liang Chen E-mail:slchern@ncepu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12174101) and the Fundamental Research Funds for the Central Universities (Grant No. 2022MS051).

摘要/Abstract

摘要： By using the numerical renormalization group (NRG) method, we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model. The dataset contains the density of states (DOS) of the host material, the strength of Coulomb interaction between on-site electrons ($U$), and the hybridization between the host material and the impurity site ($\varGamma$). The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions, respectively. From this dataset, we build seven different machine learning networks to predict the spectral function from the input data, DOS, $U$, and $\varGamma$. Three different evaluation indexes, mean absolute error (MAE), relative error (RE) and root mean square error (RMSE), are used to analyze the prediction abilities of different network models. Detailed analysis shows that, for the two kinds of widely used recurrent neural networks (RNNs), gate recurrent unit (GRU) has better performance than the long short term memory (LSTM) network. A combination of bidirectional GRU (BiGRU) and GRU has the best performance among GRU, BiGRU, LSTM, and BiLSTM. The MAE peak of ${\rm BiGRU+GRU}$ reaches 0.00037. We have also tested a one-dimensional convolutional neural network (1DCNN) with 20 hidden layers and a residual neural network (ResNet), we find that the 1DCNN has almost the same performance of the $\rm BiGRU+GRU$ network for the original dataset, while the robustness testing seems to be a little weak than ${\rm BiGRU+GRU}$ when we test all these models on two other independent datasets. The ResNet has the worst performance among all the seven network models. The datasets presented in this paper, including the large data set of the spectral function of Anderson quantum impurity model, are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.

关键词: machine learning, Anderson impurity model, spectral function

Abstract: By using the numerical renormalization group (NRG) method, we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model. The dataset contains the density of states (DOS) of the host material, the strength of Coulomb interaction between on-site electrons ($U$), and the hybridization between the host material and the impurity site ($\varGamma$). The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions, respectively. From this dataset, we build seven different machine learning networks to predict the spectral function from the input data, DOS, $U$, and $\varGamma$. Three different evaluation indexes, mean absolute error (MAE), relative error (RE) and root mean square error (RMSE), are used to analyze the prediction abilities of different network models. Detailed analysis shows that, for the two kinds of widely used recurrent neural networks (RNNs), gate recurrent unit (GRU) has better performance than the long short term memory (LSTM) network. A combination of bidirectional GRU (BiGRU) and GRU has the best performance among GRU, BiGRU, LSTM, and BiLSTM. The MAE peak of ${\rm BiGRU+GRU}$ reaches 0.00037. We have also tested a one-dimensional convolutional neural network (1DCNN) with 20 hidden layers and a residual neural network (ResNet), we find that the 1DCNN has almost the same performance of the $\rm BiGRU+GRU$ network for the original dataset, while the robustness testing seems to be a little weak than ${\rm BiGRU+GRU}$ when we test all these models on two other independent datasets. The ResNet has the worst performance among all the seven network models. The datasets presented in this paper, including the large data set of the spectral function of Anderson quantum impurity model, are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.

Key words: machine learning, Anderson impurity model, spectral function

中图分类号: (Theories and models of many-electron systems)

71.10.-w

71.27.+a (Strongly correlated electron systems; heavy fermions) 75.20.Hr (Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions) 89.20.Ff (Computer science and technology)

Ting Liu(刘婷), Rong-Sheng Han(韩榕生), and Liang Chen(陈亮). Prediction of impurity spectrum function by deep learning algorithm[J]. 中国物理B, 2024, 33(5): 57102-057102.

Ting Liu(刘婷), Rong-Sheng Han(韩榕生), and Liang Chen(陈亮). Prediction of impurity spectrum function by deep learning algorithm[J]. Chin. Phys. B, 2024, 33(5): 57102-057102.

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Prediction of impurity spectrum function by deep learning algorithm

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