| GENERAL |
|
|
|
|
Network-Initialized Monte Carlo Based on Generative Neural Networks |
| Hongyu Lu1, Chuhao Li2,3, Bin-Bin Chen1, Wei Li4,5*, Yang Qi6,7*, and Zi Yang Meng1* |
1Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong, China
2Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
3School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
4Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
5School of Physics, Beihang University, Beijing 100191, China
6State Key Laboratory of Surface Physics, Fudan University, Shanghai 200438, China
7Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China
|
|
| Cite this article: |
|
Hongyu Lu, Chuhao Li, Bin-Bin Chen et al 2022 Chin. Phys. Lett. 39 050701 |
|
|
|
|
Abstract We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation from which only short Markov chains are needed before making measurements for physical observables, irrespective of the system locating at the classical critical point, fermionic Mott insulator, Dirac semimetal, or quantum critical point. We further propose a network-initialized Monte Carlo scheme based on such neural networks, which provides independent samplings and can accelerate the Monte Carlo simulations by significantly reducing the thermalization process. We demonstrate the performance of our approach on the two-dimensional Ising and fermion Hubbard models, expect that it can systematically speed up the Monte Carlo simulations especially for the very challenging many-electron problems.
|
|
|
Received: 16 February 2022
Published: 29 April 2022
|
|
| PACS: |
07.05.Tp
|
(Computer modeling and simulation)
|
| |
75.40.Mg
|
(Numerical simulation studies)
|
| |
89.70.Eg
|
(Computational complexity)
|
| |
05.70.Jk
|
(Critical point phenomena)
|
|
|
|
|
|
| [1] | Blankenbecler R, Scalapino D J, and Sugar R L 1981 Phys. Rev. D 24 2278 |
| [2] | Hirsch J E 1983 Phys. Rev. B 28 4059 |
| [3] | Hirsch J E 1985 Phys. Rev. B 31 4403 |
| [4] | Assaad F F and Evertz H G 2008 World-Line and Determinantal Quantum Monte Carlo Methods for Spins, Phonons and Electrons (Berlin: Springer) p 277 |
| [5] | Xu X Y, Liu Z H, Pan G, Qi Y, Sun K, and Meng Z Y 2019 J. Phys.: Condens. Matter 31 463001 |
| [6] | Scalettar R T, Bickers N E, and Scalapino D J 1989 Phys. Rev. B 40 197 |
| [7] | Noack R M, Scalapino D J, and Scalettar R T 1991 Phys. Rev. Lett. 66 778 |
| [8] | Chen C, Xu X Y, Liu J, Batrouni G, Scalettar R, and Meng Z Y 2018 Phys. Rev. B 98 041102(R) |
| [9] | Chen C, Xu X Y, Meng Z Y, and Hohenadler M 2019 Phys. Rev. Lett. 122 077601 |
| [10] | Xu X Y, Sun K, Schattner Y, Berg E, and Meng Z Y 2017 Phys. Rev. X 7 031058 |
| [11] | Liu Z H, Pan G, Xu X Y, Sun K, and Meng Z Y 2019 Proc. Natl. Acad. Sci. USA 116 16760 |
| [12] | Jiang W, Liu Y, Klein A, Wang Y, Sun K, Chubukov A V, and Meng Z Y 2021 arXiv:2105.03639 [cond-mat.str-el] |
| [13] | Liu Y, Jiang W, Klein A, Wang Y, Sun K, Chubukov A V, and Meng Z Y 2022 Phys. Rev. B 105 L041111 |
| [14] | Zhang X, Pan G, Zhang Y, Kang J, and Meng Z Y 2021 Chin. Phys. Lett. 38 077305 |
| [15] | Hofmann J S, Khalaf E, Vishwanath A, Berg E, and Lee J Y 2021 arXiv:2105.12112 [cond-mat.str-el] |
| [16] | Pan G, Zhang X, Li H, Sun K, and Meng Z Y 2022 Phys. Rev. B 105 L121110 |
| [17] | Zhang X, Sun K, Li H, Pan G, and Meng Z Y 2021 arXiv:2111.10018 [cond-mat.str-el] |
| [18] | Swendsen R H and Wang J S 1987 Phys. Rev. Lett. 58 86 |
| [19] | Wolff U 1989 Phys. Rev. Lett. 62 361 |
| [20] | Sandvik A W 1999 Phys. Rev. B 59 R14157 |
| [21] | Prokof'ev N V, Svistunov B V, and Tupitsyn I S 1998 J. Exp. Theor. Phys. 87 310 |
| [22] | Prokof'ev N V, Svistunov B V, and Tupitsyn I S 1998 Phys. Lett. A 238 253 |
| [23] | Sandvik A W 2010 AIP Conf. Proc. 1297 135 |
| [24] | Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt-Maranto L, and Zdeborová L 2019 Rev. Mod. Phys. 91 045002 |
| [25] | Carrasquilla J 2020 Adv. Phys.: X 5 1797528 |
| [26] | Bedolla E, Padierna L C, and Casta P R 2020 J. Phys.: Condens. Matter 33 053001 |
| [27] | Ch'ng K, Carrasquilla J, Melko R G, and Khatami E 2017 Phys. Rev. X 7 031038 |
| [28] | Broecker P, Carrasquilla J, Melko R G, and Trebst S 2017 Sci. Rep. 7 8823 |
| [29] | Carrasquilla J and Melko R G 2017 Nat. Phys. 13 431 |
| [30] | Carleo G, Nomura Y, and Imada M 2018 Nat. Commun. 9 5322 |
| [31] | Carleo G and Troyer M 2017 Science 355 602 |
| [32] | Cai Z and Liu J 2018 Phys. Rev. B 97 035116 |
| [33] | Choo K, Carleo G, Regnault N, and Neupert T 2018 Phys. Rev. Lett. 121 167204 |
| [34] | Cheng S, Wang L, Xiang T, and Zhang P 2019 Phys. Rev. B 99 155131 |
| [35] | Guo C, Jie Z, Lu W, and Poletti D 2018 Phys. Rev. E 98 042114 |
| [36] | Han Z Y, Wang J, Fan H, Wang L, and Zhang P 2018 Phys. Rev. X 8 031012 |
| [37] | Xie H, Zhang L, and Wang L 2022 J. Mach. Learn. Res. 1 38 |
| [38] | Efthymiou S, Beach M J S, and Melko R G 2019 Phys. Rev. B 99 075113 |
| [39] | Liu J, Qi Y, Meng Z Y, and Fu L 2017 Phys. Rev. B 95 041101(R) |
| [40] | Liu J, Shen H, Qi Y, Meng Z Y, and Fu L 2017 Phys. Rev. B 95 241104(R) |
| [41] | Xu X Y, Qi Y, Liu J, Fu L, and Meng Z Y 2017 Phys. Rev. B 96 041119(R) |
| [42] | Nagai Y, Shen H, Qi Y, Liu J, and Fu L 2017 Phys. Rev. B 96 161102(R) |
| [43] | Huang L and Wang L 2017 Phys. Rev. B 95 035105 |
| [44] | Huang L, Yang Y F, and Wang L 2017 Phys. Rev. E 95 031301(R) |
| [45] | Endo K, Nakamura T, Fujii K, and Yamamoto N 2020 Phys. Rev. Res. 2 043442 |
| [46] | Liu Z H, Xu X Y, Qi Y, Sun K, and Meng Z Y 2018 Phys. Rev. B 98 045116 |
| [47] | Liu Z H, Xu X Y, Qi Y, Sun K, and Meng Z Y 2019 Phys. Rev. B 99 085114 |
| [48] | Zhang L, E W, and Wang L 2018 arXiv:1809.10188 [cs.LG] |
| [49] | Hartnett G S and Mohseni M 2020 arXiv:2001.00585 [cs.LG] |
| [50] | Li S H and Wang L 2018 Phys. Rev. Lett. 121 260601 |
| [51] | Wu D, Wang L, and Zhang P 2019 Phys. Rev. Lett. 122 080602 |
| [52] | Sharir O, Levine Y, Wies N, Carleo G, and Shashua A 2020 Phys. Rev. Lett. 124 020503 |
| [53] | Liu J G, Mao L, Zhang P, and Wang L 2021 Mach. Learn.: Sci. Technol. 2 025011 |
| [54] | Alcalde P D and Eremin I M 2020 Phys. Rev. B 102 195148 |
| [55] | Albergo M S, Kanwar G, and Shanahan P E 2019 Phys. Rev. D 100 034515 |
| [56] | McNaughton B, Milošević M V, Perali A, and Pilati S 2020 Phys. Rev. E 101 053312 |
| [57] | Singh J, Arora V, Gupta V, and Scheurer M S 2021 SciPost Phys. 11 043 |
| [58] | Wu D, Rossi R, and Carleo G 2021 Phys. Rev. Res. 3 L042024 |
| [59] | Goodfellow I J et al. 2014 NIPS'14: Proceedings of the 27th International Conference on Neural Information Processing Systems vol 2 pp 2672–2680 |
| [60] | Meng Z Y, Lang T C, Wessel S, Assaad F F, and Muramatsu A 2010 Nature 464 847 |
| [61] | Sorella S, Otsuka Y, and Yunoki S 2012 Sci. Rep. 2 992 |
| [62] | Assaad F F and Herbut I F 2013 Phys. Rev. X 3 031010 |
| [63] | Lang T C and Läuchli A M 2019 Phys. Rev. Lett. 123 137602 |
| [64] | Liu Y, Wang W, Sun K, and Meng Z Y 2020 Phys. Rev. B 101 064308 |
| [65] | Abadi M et al. 2016 arXiv:1603.04467 [cs.DC] |
| [66] | Kingma D P and Ba J 2015 arXiv:1412.6980 [cs.LG] |
| [67] | Liao Y D, Xu X Y, Meng Z Y, and Kang J 2021 Chin. Phys. B 30 017305 |
| [68] | Liao Y D, Kang J, Breiø C N, Xu X Y, Wu H Q, Andersen B M, Fernandes R M, and Meng Z Y 2021 Phys. Rev. X 11 011014 |
| [69] | Liao Y D, Meng Z Y, and Xu X Y 2019 Phys. Rev. Lett. 123 157601 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
