Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field

doi:10.1088/1674-1056/ae1564

中国物理B ›› 2025, Vol. 34 ›› Issue (12): 127504-127504.doi: 10.1088/1674-1056/ae1564

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Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field

Yun-Tong Yang(杨贇彤)^1,2, Fu-Zhou Chen(陈富州)^1,2, and Hong-Gang Luo(罗洪刚)^1,2,†

1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China

收稿日期:2025-07-04 修回日期:2025-09-04 接受日期:2025-10-21 发布日期:2025-11-25
通讯作者: Hong-Gang Luo E-mail:luohg@lzu.edu.cn
基金资助:
The work is partly supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402704) and the National Natural Science Foundation of China (Grant No. 12247101).

Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field

Yun-Tong Yang(杨贇彤)^1,2, Fu-Zhou Chen(陈富州)^1,2, and Hong-Gang Luo(罗洪刚)^1,2,†

1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China

Received:2025-07-04 Revised:2025-09-04 Accepted:2025-10-21 Published:2025-11-25
Contact: Hong-Gang Luo E-mail:luohg@lzu.edu.cn
About author:2025-127504-251151.pdf
Supported by:
The work is partly supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402704) and the National Natural Science Foundation of China (Grant No. 12247101).

摘要/Abstract

摘要： A uniform longitudinal field applied to the transverse Ising model (TIM) distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart. While the ground state of the latter shows no quantum phase transition (QPT), the ground state of the former exhibits rich phases: paramagnetic, antiferromagnetic, and possibly disordered phases. Although the first two are clearly identified, the existence of the disordered phase remains controversial. Here, we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction $J$, the transverse field $h_x$ and the longitudinal field $h_z$, and uncover which patterns are responsible for these three competing energy scales, thereby determining the possible phases and the QPTs among them. The system size ranges from $L=8$ to $128$ and the transverse field $h_x$ is fixed at $1$. Under these parameters, our results show the existence of the disordered phase. For a small $h_z$, the system transitions from a disordered phase to an antiferromagnetic phase as $J$ increases. For a large $h_z$, the system undergoes two phase transitions: from paramagnetic to disordered, and then to antiferromagnetic phase. These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.

关键词: pattern picture, quantum phase transitions, antiferromagnetic Ising model

Abstract: A uniform longitudinal field applied to the transverse Ising model (TIM) distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart. While the ground state of the latter shows no quantum phase transition (QPT), the ground state of the former exhibits rich phases: paramagnetic, antiferromagnetic, and possibly disordered phases. Although the first two are clearly identified, the existence of the disordered phase remains controversial. Here, we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction $J$, the transverse field $h_x$ and the longitudinal field $h_z$, and uncover which patterns are responsible for these three competing energy scales, thereby determining the possible phases and the QPTs among them. The system size ranges from $L=8$ to $128$ and the transverse field $h_x$ is fixed at $1$. Under these parameters, our results show the existence of the disordered phase. For a small $h_z$, the system transitions from a disordered phase to an antiferromagnetic phase as $J$ increases. For a large $h_z$, the system undergoes two phase transitions: from paramagnetic to disordered, and then to antiferromagnetic phase. These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.

Key words: pattern picture, quantum phase transitions, antiferromagnetic Ising model

中图分类号: (Spin chain models)

75.10.Pq

75.40.Mg (Numerical simulation studies) 68.35.Rh (Phase transitions and critical phenomena)

Yun-Tong Yang(杨贇彤), Fu-Zhou Chen(陈富州), and Hong-Gang Luo(罗洪刚). Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field[J]. 中国物理B, 2025, 34(12): 127504-127504.

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Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field

Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field

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