Solving quantum rotor model with different Monte Carlo techniques

doi:10.1088/1674-1056/ac4f52

中国物理B ›› 2022, Vol. 31 ›› Issue (4): 40504-040504.doi: 10.1088/1674-1056/ac4f52

Solving quantum rotor model with different Monte Carlo techniques

Weilun Jiang(姜伟伦)^1,2, Gaopei Pan(潘高培)^1,2, Yuzhi Liu(刘毓智)^1,2, and Zi-Yang Meng(孟子杨)^3,1,4,†

1 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
3 Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China;
4 Songshan Lake Materials Laboratory, Dongguan 523808, China

收稿日期:2021-12-05 修回日期:2022-01-25 接受日期:2022-01-27 出版日期:2022-03-16 发布日期:2022-03-29
通讯作者: Zi-Yang Meng E-mail:zymeng@hku.hk
基金资助:
We thank Ying-Jer Kao for insightful discussion and introduction to us the over-relaxation update scheme in Ref.[5]. WLJ, GPP, YZL and ZYM acknowledge the supports from the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000) and the RGC of Hong Kong SAR of China (Grant Nos. 17303019, 17301420, and AoE/P-701/20). We thank the Center for Quantum Simulation Sciences in the Institute of Physics, Chinese Academy of Sciences, the Computational Initiative at the Faculty of Science at the University of Hong Kong, the National Supercomputer Center in Tianjin, and the National Supercomputer Center in Guangzhou for their technical support and generous allocation of CPU time.

Solving quantum rotor model with different Monte Carlo techniques

Weilun Jiang(姜伟伦)^1,2, Gaopei Pan(潘高培)^1,2, Yuzhi Liu(刘毓智)^1,2, and Zi-Yang Meng(孟子杨)^3,1,4,†

1 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
3 Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China;
4 Songshan Lake Materials Laboratory, Dongguan 523808, China

Received:2021-12-05 Revised:2022-01-25 Accepted:2022-01-27 Online:2022-03-16 Published:2022-03-29
Contact: Zi-Yang Meng E-mail:zymeng@hku.hk
Supported by:
We thank Ying-Jer Kao for insightful discussion and introduction to us the over-relaxation update scheme in Ref.[5]. WLJ, GPP, YZL and ZYM acknowledge the supports from the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000) and the RGC of Hong Kong SAR of China (Grant Nos. 17303019, 17301420, and AoE/P-701/20). We thank the Center for Quantum Simulation Sciences in the Institute of Physics, Chinese Academy of Sciences, the Computational Initiative at the Faculty of Science at the University of Hong Kong, the National Supercomputer Center in Tianjin, and the National Supercomputer Center in Guangzhou for their technical support and generous allocation of CPU time.

摘要/Abstract

摘要： We systematically test the performance of several Monte Carlo update schemes for the (2+1)d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) schemes, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z₂ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

关键词: Monte Carlo methods

Abstract: We systematically test the performance of several Monte Carlo update schemes for the (2+1)d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) schemes, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z₂ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

Key words: Monte Carlo methods

中图分类号: (Monte Carlo methods)

05.10.Ln

Weilun Jiang(姜伟伦), Gaopei Pan(潘高培), Yuzhi Liu(刘毓智), and Zi-Yang Meng(孟子杨). Solving quantum rotor model with different Monte Carlo techniques[J]. 中国物理B, 2022, 31(4): 40504-040504.

Weilun Jiang(姜伟伦), Gaopei Pan(潘高培), Yuzhi Liu(刘毓智), and Zi-Yang Meng(孟子杨). Solving quantum rotor model with different Monte Carlo techniques[J]. Chin. Phys. B, 2022, 31(4): 40504-040504.

参考文献

[1] José J V, Kadanoff L P, Kirkpatrick S and Nelson D R 1977 Phys. Rev. B 16 1217
[2] Wallin M, Sørensen E S, Girvin S M and Young A P 1994 Phys. Rev. B 49 12115
[3] Hasenbusch M and Török T 1999 J. Phys. A:Math. Gen. 32 6361
[4] Hasenbusch M 2019 Phys. Rev. B 100 224517
[5] Lan T Y, Hsieh Y D and Kao Y J 2012 arXiv:1211.0780[cond- mat.stat-mech]
[6] Xu W, Sun Y, Lv J P and Deng Y 2019 Phys. Rev. B 100 064525
[7] Campostrini M, Hasenbusch M, Pelissetto A, Rossi P and Vicari E 2001 Phys. Rev. B 63 214503
[8] Campostrini M, Hasenbusch M, Pelissetto A and Vicari E 2006 Phys. Rev. B 74 144506
[9] Chester S M, Landry W, Liu J, Poland D, Simmons-Duffin D, Su N and Vichi A 2020 Journal of High Energy Physics 2020 142
[10] Fisher M P A and Grinstein G 1988 Phys. Rev. Lett. 60 208
[11] Cha M C, Fisher M P A, Girvin S M, Wallin M and Young A P 1991 Phys. Rev. B 44 6883
[12] Fisher M P A, Weichman P B, Grinstein G and Fisher D S 1989 Phys. Rev. B 40 546
[13] Greiner M, Mandel O, Esslinger T, Hänsch T W and Bloch I 2002 Nature 415 39
[14] Meng Z Y and Wessel S 2008 Phys. Rev. B 78 224416
[15] 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 1
[16] 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
[17] Da Liao Y, Li H, Yan Z, Wei H T, Li W, Qi Y and Meng Z Y 2021 Phys. Rev. B 103 104416
[18] Swendsen R H and Wang J S 1987 Phys. Rev. Lett. 58 86
[19] Wolff U 1989 Phys. Rev. Lett. 62 361
[20] Adler S L 1981 Phys. Rev. D 23 2901
[21] Alet F and Sørensen E S 2003 Phys. Rev. E 68 026702
[22] Xu X Y, Sun K, Schattner Y, Berg E and Meng Z Y 2017 Phys. Rev. X 7 031058
[23] Liu Z H, Pan G, Xu X Y, Sun K and Meng Z Y 2019 Proc. Natl. Acad. Sci. USA 116 16760
[24] Xu X Y, Qi Y, Zhang L, Assaad F F, Xu C and Meng Z Y 2019 Phys. Rev. X 9 021022
[25] Wang W, Lu D C, Xu X Y, You Y Z and Meng Z Y 2019 Phys. Rev. B 100 085123
[26] Xu X Y, Liu Z H, Pan G, Qi Y, Sun K and Meng Z Y 2019 J. Phys.:Condens. Matter 31 463001
[27] Liu J, Qi Y, Meng Z Y and Fu L 2017 Phys. Rev. B 95 041101
[28] Xu X Y, Qi Y, Liu J, Fu L and Meng Z Y 2017 Phys. Rev. B 96 041119
[29] Lu H, Li C, Li W, Qi Y and Meng Z Y 2021 arXiv:2106.00712[cond- mat.str-el]
[30] Fisher M P A 1989 Phys. Rev. Lett. 62 1415
[31] Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H and Teller E 1953 The Journal of Chemical Physics 21 1087
[32] Davies C, Batrouni G, Katz G, Kronfeld A, Lepage P, Rossi P, Svetitsky B and Wilson K 1986 J. Stat. Phys. 43 1073
[33] Ferreira A L and Toral R 1993 Phys. Rev. E 47 R3848
[34] Duane S, Kennedy A D, Pendleton B J and Roweth D 1988 Phys. Lett. B 195 216
[35] Catterall S and Karamov S 2002 Phys. Lett. B 528 301
[36] Batrouni G G, Katz G R, Kronfeld A S, Lepage G P, Svetitsky B and Wilson K G 1985 Phys. Rev. D 32 2736
[37] Hastings W K 1970 Biometrika 57 97
[38] Whitmer C 1984 Phys. Rev. D 29 306
[39] Duane S, Kennedy A, Pendleton B J and Roweth D 1987 Phys. Lett. B 195 216
[40] Gupta R, Kilcup G W and Sharpe S R 1988 Phys. Rev. D 38 1278
[41] Mehlig B, Heermann D W and Forrest B M 1992 Phys. Rev. B 45 679
[42] Scalettar R T, Scalapino D J, Sugar R L and Toussaint D 1987 Phys. Rev. B 36 8632
[43] Beyl S, Goth F and Assaad F F 2018 Phys. Rev. B 97 085144
[44] Batrouni G G and Scalettar R T 2019 Phys. Rev. B 99 035114
[45] Bradley O, Batrouni G G and Scalettar R T 2021 Phys. Rev. B 103 235104
[46] Senthil T and Motrunich O 2002 Phys. Rev. B 66 205104
[47] Paramekanti A and Vishwanath A 2004 Phys. Rev. B 70 245118
[48] Chen C, Xu X Y, Qi Y and Meng Z Y 2020 Chin. Phys. Lett. 37 047103
[49] Gazit S, Assaad F F and Sachdev S 2020 Phys. Rev. X 10 041057
[50] Chen C, Yuan T, Qi Y and Meng Z Y 2021 Phys. Rev. B 103 165131
[51] Dupuis E, Paranjape M B and Witczak-Krempa W 2019 Phys. Rev. B 100 094443
[52] Zhang X, Pan G, Zhang Y, Kang J and Meng Z Y 2021 Chin. Phys. Lett. 38 077305
[53] 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]
[54] Liu Y, Jiang W, Klein A, Wang Y, Sun K, Chubukov A V and Meng Z Y 2022 Phys. Rev. B 105 L041111
[55] Sandvik A W and Zhao B 2020 Chin. Phys. Lett. 37 057502

Solving quantum rotor model with different Monte Carlo techniques

Solving quantum rotor model with different Monte Carlo techniques

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

Metrics

本文评价

推荐阅读 0