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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 |
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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.
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Received: 05 December 2021
Revised: 25 January 2022
Accepted manuscript online: 27 January 2022
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PACS:
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05.10.Ln
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(Monte Carlo methods)
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| Fund: 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. |
Corresponding Authors:
Zi-Yang Meng
E-mail: zymeng@hku.hk
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Cite this article:
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 2022 Chin. Phys. B 31 040504
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