Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

doi:10.1088/1674-1056/ad1d4d

中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40503-040503.doi: 10.1088/1674-1056/ad1d4d

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

Heyang Ma(马赫阳)¹, Wanzhou Zhang(张万舟)^1,2,†, Yanting Tian(田彦婷)¹, Chengxiang Ding(丁成祥)³, and Youjin Deng(邓友金)^2,4,5,‡

1 College of Physics, Taiyuan University of Technology, Taiyuan 030024, China;
2 Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
3 School of Microelectronics & Data Science, Anhui University of Technology, Maanshan 243002, China;
4 Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China;
5 Shanghai Research Center for Quantum Sciences, Shanghai 201315, China

收稿日期:2023-11-08 修回日期:2024-01-09 接受日期:2024-01-11 出版日期:2024-03-19 发布日期:2024-04-01
通讯作者: Wanzhou Zhang, Youjin Deng E-mail:zhangwanzhou@tyut.edu.cn;yjdeng@ustc.edu.cn
基金资助:
Project supported by the Hefei National Research Center for Physical Sciences at the Microscale (Grant No. KF2021002), the Natural Science Foundation of Shanxi Province, China (Grant Nos. 202303021221029 and 202103021224051), the National Natural Science Foundation of China (Grant Nos. 11975024, 12047503, and 12275263), the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities (Grant No. gxyqZD2019023), and the National Key Research and Development Program of China (Grant No. 2018YFA0306501).

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

Heyang Ma(马赫阳)¹, Wanzhou Zhang(张万舟)^1,2,†, Yanting Tian(田彦婷)¹, Chengxiang Ding(丁成祥)³, and Youjin Deng(邓友金)^2,4,5,‡

1 College of Physics, Taiyuan University of Technology, Taiyuan 030024, China;
2 Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
3 School of Microelectronics & Data Science, Anhui University of Technology, Maanshan 243002, China;
4 Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China;
5 Shanghai Research Center for Quantum Sciences, Shanghai 201315, China

Received:2023-11-08 Revised:2024-01-09 Accepted:2024-01-11 Online:2024-03-19 Published:2024-04-01
Contact: Wanzhou Zhang, Youjin Deng E-mail:zhangwanzhou@tyut.edu.cn;yjdeng@ustc.edu.cn
Supported by:
Project supported by the Hefei National Research Center for Physical Sciences at the Microscale (Grant No. KF2021002), the Natural Science Foundation of Shanxi Province, China (Grant Nos. 202303021221029 and 202103021224051), the National Natural Science Foundation of China (Grant Nos. 11975024, 12047503, and 12275263), the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities (Grant No. gxyqZD2019023), and the National Key Research and Development Program of China (Grant No. 2018YFA0306501).

摘要/Abstract

摘要： The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

关键词: topological phase transition, Ising-XY model, Monte Carlo method, half vortex

Abstract: The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

Key words: topological phase transition, Ising-XY model, Monte Carlo method, half vortex

中图分类号: (Classical statistical mechanics)

05.20.-y

05.10.Ln (Monte Carlo methods) 74.25.Ha (Magnetic properties including vortex structures and related phenomena) 87.16.aj (Lattice models)

Heyang Ma(马赫阳), Wanzhou Zhang(张万舟), Yanting Tian(田彦婷), Chengxiang Ding(丁成祥), and Youjin Deng(邓友金). Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method[J]. 中国物理B, 2024, 33(4): 40503-040503.

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Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

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