|
|
|
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 |
|
|
|
|
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.
|
Received: 01 December 2023
Revised: 09 March 2024
Accepted manuscript online: 29 March 2024
|
|
PACS:
|
71.10.-w
|
(Theories and models of many-electron systems)
|
| |
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)
|
|
| Fund: 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). |
Corresponding Authors:
Liang Chen
E-mail: slchern@ncepu.edu.cn
|
Cite this article:
Ting Liu(刘婷), Rong-Sheng Han(韩榕生), and Liang Chen(陈亮) Prediction of impurity spectrum function by deep learning algorithm 2024 Chin. Phys. B 33 057102
|
[1] Anderson P W 1961 Phys. Rev. 124 41
[2] Anderson P W 1970 J. Phys. C Solid State Phys. 3 2436
[3] Georges A, Kotliar G, Krauth W and Rozenberg M J 1996 Rev. Mod. Phys. 68 13
[4] Wiegmann P B and Tsvelick A M 1983 J. Phys. C Solid State Phys. 16 2281
[5] Tsvelick A M and Wiegmann P B 1983 Adv. Phys. 32 453
[6] Affleck I 1990 Nucl. Phys. B 336 517
[7] Affleck I 2009 arXiv:0809.3474v2
[cond-mat.str-el]
[8] Coleman P 1984 Phys. Rev. B 29 3035
[9] Coleman P 1984 Phys. Rev. B 35 5072
[10] Pruschke Z and Grewe N 1989 Z. Phys. B: Condens. Matter 74 439
[11] Haule K, Kirchner S, Kroha J and Wölfle P 2001 Phys. Rev. B 64 155111
[12] Tosi L, Roura-Bas P, Llois A M and Manuel L O 2011 Phys. Rev. B 83 073301
[13] Wilson K G 1975 Rev. Mod. Phys. 47 773
[14] Bulla R, Costi T A and Pruschke T 2008 Rev. Mod. Phys. 80 395
[15] Hirsch J E 1983 Phys. Rev. B 28 4059
[16] Hirsch J E and Fye R M 1986 Phys. Rev. Lett. 56 2521
[17] Fye R M and Hirsch J E 1988 Phys. Rev. B 38 433
[18] Rubtsov A N, Savkin V V and Lichtenstein A I 2005 Phys. Rev. B 72 035122
[19] Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, VogtMaranto L and Zdeborová L 2019 Rev. Mod. Phys. 91 045002
[20] Medeiros L, Psaltis D, Lauer T R and Ozel F 2023 Astrophys. J. Lett. 947 L7
[21] Karagiorgi G, Kasieczka G, Kravitz S, Nachman B P and Shih D 2021 Nat. Rev. Phys. 4 399
[22] Boehnlein A, Diefenthaler M, Sato N, Schram M, Ziegler V, Fanelli C, Hjorth-Jensen M, Horn T, Kuchera M P, Lee D, Nazarewicz W, Ostroumov P, Orginos K, Poon A, Wang X N, Scheinker A, Smith M S and Pang L G 2022 Rev. Mod. Phys. 94 031003
[23] Carrasquilla J and Melko R G 2017 Nat. Phys. 13 431
[24] Rodriguez-Nieva J F and Scheurer M S 2019 Nat. Phys. 15 790
[25] Lustig E, Yair O, Talmon R and Segev M 2020 Phys. Rev. Lett. 125 127401
[26] Huang L and Wang L 2017 Phys. Rev. B 95 035105
[27] Schleder G R, Padilha A C M, Acosta C M, Costa M and Fazzio A 2019 J. Phys.: Mater. 2 032001
[28] Brockherde F, Vogt L, Li L, Tuckerman M E, Burke K and Müller K R 2017 Nat. Commun. 8 872
[29] Butler K T, Davies D W, Cartwright H, Isayev O and Walsh A 2018 Nature 559 547
[30] Schütt K T, Sauceda H E, Kindermans P J, Tkatchenko A and Müller K R 2018 J. Chem. Phys. 148 241722
[31] Xie T and Grossman J C 2018 Phys. Rev. Lett. 120 145301
[32] Arsenault L F, Lopez-Bezanilla A, von Lilienfeld O A and Millis A J 2014 Phys. Rev. B 90 155136
[33] Sturm E J, Carbone M R, Lu D, Weichselbaum A and Konik R M 2021 Phys. Rev. B 103 245118
[34] Walker N, Kellar S, Zhang Y, Tam K M and Moreno J 2022 Crystals 12 1269
[35] Ren X Y, Han R S and Chen L 2021 J. Phys. Condens. Matter 33 495601
[36] Miles C, Carbone M R, Sturm E J, Lu D, Weichselbaum A, Barros K and Konik R M 2021 Phys. Rev. B 104 235111
[37] Žitko R and Pruschke T 2009 Phys. Rev. B 79 085106
[38] Weiße A, Wellein G, Alvermann A and Fehske H 2006 Rev. Mod. Phys. 78 275
[39] Hochreiter S and Schmidhuber J 1997 Neural Comput. 9 1735
[40] Cho K, van Merriënboer B, Gulcehre C, Bahdanau D, Bougares F, Schwenk H and Bengio Y 2014 Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), Doha, Qatar, pp. 1724-1734
[41] Hinton G E, Srivastava N, Krizhevsky A, Sutskever I and Salakhutdinov R R 2012 arXiv:1207.0580v1[cs.NE] |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
