|
|
|
Auxiliary-field Monte Carlo method for frustrated spin systems |
| Ning Cai(蔡凝)1, Yuan Gao(高源)2,3, Wei Li(李伟)3,4†, and Yang Qi(戚扬)1‡ |
1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China;
2 School of Physics, Beihang University, Beijing 100191, China;
3 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
4 Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China |
|
|
|
|
Abstract We extend a semiclassical numerical method, bosonic auxiliary-field Monte Carlo, to quantum spin systems. This method breaks the lattice into clusters, solves each cluster precisely and couples them with classical auxiliary fields through classical Monte Carlo simulation. We test the method with antiferromagnetic spin models in one-dimensional chains, square lattices and triangular lattices, and obtain reasonable results at finite temperatures. This algorithm builds a bridge between classical Monte Carlo method and quantum methods. The algorithm can be improved with either progress in classical Monte Carlo sampling or the development of quantum solvers, and can also be further applied to systems with different lattices or interactions.
|
Received: 05 December 2024
Revised: 05 December 2024
Accepted manuscript online: 08 January 2025
|
|
PACS:
|
75.10.Jm
|
(Quantized spin models, including quantum spin frustration)
|
| |
87.55.K-
|
(Monte Carlo methods)
|
|
| Fund: W.L. acknowledges supports by the National Key Research and Development Program of China (Grant No. 2024YFA1409200), the National Natural Science Foundation of China (Grant Nos. 12222412 and 12047503), and CAS Project for Young Scientists in Basic Research (Grant No. YSBR-057). Y.Q. acknowledges supports by the National Natural Science Foundation of China (Grant No. 12374144). |
Corresponding Authors:
Wei Li, Yang Qi
E-mail: w.li@itp.ac.cn;qiyang@fudan.edu.cn
|
Cite this article:
Ning Cai(蔡凝), Yuan Gao(高源), Wei Li(李伟), and Yang Qi(戚扬) Auxiliary-field Monte Carlo method for frustrated spin systems 2025 Chin. Phys. B 34 027504
|
[1] Diep H T 2020 Frustrated Spin Systems, 3rd Ed.(World Scientific)
[2] Xiang J, Zhang C, Gao Y, Schmidt W, Schmalzl K, Wang C W, Li B, Xi N, Liu X Y, Jin H, Li G, Shen J, Chen Z, Qi Y, Wan Y, Jin W, Li W, Sun P and Su G 2024 Nature 625 270
[3] Shangguan Y, Bao S, Dong Z Y, et al. 2023 Nat. Phys. 19 1883
[4] Balents L 2010 Nature 464 199
[5] Zhou Y, Kanoda K and Ng T K 2017 Rev. Mod. Phys. 89 025003
[6] Broholm C, Cava R J, Kivelson S A, Nocera D G, Norman M R and Senthil T 2020 Science 367 eaay0668
[7] Wen J, Yu S L, Li S, Yu W and Li J X 2019 npj Quantum Mater. 4 12
[8] Bramwell S T and Gingras M J P 2001 Science 294 1495
[9] Castelnovo C, Moessner R and Sondhi S L 2011 Annu. Rev. Condens. Matter Phys. 3 35
[10] Gingras M J P and McClarty P A 2014 Rep. Prog. Phys. 77 056501
[11] Shen Y, Liu C, Qin Y, Shen S, Li Y D, Bewley R, Schneidewind A, Chen G and Zhao J 2020 Nat. Commun. 10 4530
[12] Li H, Liao Y D, Chen B B, Zeng X T, Sheng X L, Qi Y, Meng Z Y and Li W 2020 Nat. Commun. 11 1111
[13] Hu Z, Ma Z, Liao Y D, Li H, Ma C, Cui Y, Shangguan Y, Huang Z, Qi Y, Li W, Meng Z Y, Wen J and Yu W 2020 Nat. Commun. 11 5631
[14] Dun Z, Daum M, Baral R, Fischer H E, Cao H, Liu Y, Stone M B, Rodriguez Rivera J A, Choi E S, Huang Q, Zhou H, Mourigal M and Frandsen B A 2021 Phys. Rev. B 103 064424
[15] Sandvik A W 2010 AIP Conf. Proc. 1297 135
[16] Pollet L 2012 Rep. Prog. Phys. 75 094501
[17] Chandrasekharan S and Wiese U J 1999 Phys. Rev. Lett. 83 3116
[18] Sato T and Assaad F F 2021 Phys. Rev. B 104 L081106
[19] White S R 1992 Phys. Rev. Lett. 69 2863
[20] White S R 1993 Phys. Rev. B 48 10345
[21] Bursill R J, Xiang T and Gehring G A 1996 J. Phys. Condens. Matter 8 L583
[22] Wang X Q and Xiang T 1997 Phys. Rev. B 56 5061
[23] Verstraete F and Cirac J I 2004 arXiv:cond-mat/0407066[cond-mat.strel]
[24] Jordan J, Orus R, Vidal G, Verstraete F and Cirac J I 2008 Phys. Rev. Lett. 101 250602
[25] Shi Y Y, Duan L M and Vidal G 2006 Phys. Rev. A 74 022320
[26] Tagliacozzo L, Evenbly G and Vidal G 2009 Phys. Rev. B 80 235127
[27] Vidal G 2007 Phys. Rev. Lett. 99 220405
[28] Vidal G 2008 Phys. Rev. Lett. 101 110501
[29] Jiang H C, Weng Z Y and Xiang T 2008 Phys. Rev. Lett. 101 090603
[30] Wang L and Frank Verstraete 2011 arXiv:1110.4362[cond-mat.str-el]
[31] Levin M and Nave C P 2007 Phys. Rev. Lett. 99 120601
[32] Xie Z Y, Jiang H C, Chen Q N, Weng Z Y and Xiang T 2009 Phys. Rev. Lett. 103 160601
[33] Gu Z C, Levin M and Wen X G 2008 Phys. Rev. B 78 205116
[34] Gu Z C and Wen X G 2009 Phys. Rev. B 80 155131
[35] Chen P, Lai C Y and Yang M F 2009 J. Stat. Mech. 2009 P10001
[36] Li W, Gong S S, Zhao Y and Su G 2010 Phys. Rev. B 81 184427
[37] Li W, Gong S S, Zhao Y, Ran S J, Gao S and Su G 2010 Phys. Rev. B 82 134434
[38] Malpetti D and Roscilde T 2017 Phys. Rev. Lett. 119 040602
[39] Ulmke M and Scalettar R T 2000 Phys. Rev. B 61 9607
[40] Sandvik A W and Kurkijarvi J 1991 Phys. Rev. B 43 5950
[41] Sandvik A W 1999 Phys. Rev. B 59 R14157
[42] Syljuasen O F and Sandvik A W 2002 Phys. Rev. E 66 046701
[43] Li Q Y, Gao Y, He Y Y, Qi Y, Chen B B and Li W 2023 Phys. Rev. Lett. 130 226502
[44] Prelovsek P and Bonca J 2013 Strongly Correlated Systems. Springer Series in Solid-State Sciences 176(Avella A and Mancini F, Ed.) (Berlin, Heidelberg:Springer)
[45] Liu J, Qi Y, Meng Z Y and Fu L 2017 Phys. Rev. B 95 041101 |
| 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
|
|
|
