| Topological Quantum Statistical Mechanics and Topological Quantum Field Theories |
| Zhang, Zhidong
|
| 通讯作者 | Zhang, Zhidong(zdzhang@imr.ac.cn)
|
| 2022-02-01
|
| 发表期刊 | SYMMETRY-BASEL
 |
| 卷号 | 14期号:2页码:22 |
| 摘要 | The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins (or particles) with Z(2) symmetry, the phenomena revealed in Ising systems may afford us lessons for other types of interactions in nature. In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan-von Neumann-Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan-von Neumann-Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry. |
| 关键词 | 3D Ising model
topology
quantum statistical mechanics
quantum field theories
|
| 资助者 | National Natural Science Foundation of China
|
| DOI | 10.3390/sym14020323
|
| 收录类别 | SCI
|
| 语种 | 英语
|
| 资助项目 | National Natural Science Foundation of China
|
| WOS研究方向 | Science & Technology - Other Topics
|
| WOS类目 | Multidisciplinary Sciences
|
| WOS记录号 | WOS:000778136900001
|
| 出版者 | MDPI
|
| 引用统计 |
|
| 文献类型 | 期刊论文
|
| 条目标识符 | http://ir.imr.ac.cn/handle/321006/173072
|
| 专题 | 中国科学院金属研究所
|
| 通讯作者 | Zhang, Zhidong |
| 作者单位 | Chinese Acad Sci, Inst Met Res, Shenyang Natl Lab Mat Sci, 72 Wenhua Rd, Shenyang 110016, Peoples R China
|
推荐引用方式
GB/T 7714 |
Zhang, Zhidong. Topological Quantum Statistical Mechanics and Topological Quantum Field Theories[J]. SYMMETRY-BASEL,2022,14(2):22.
|
| APA |
Zhang, Zhidong.(2022).Topological Quantum Statistical Mechanics and Topological Quantum Field Theories.SYMMETRY-BASEL,14(2),22.
|
| MLA |
Zhang, Zhidong."Topological Quantum Statistical Mechanics and Topological Quantum Field Theories".SYMMETRY-BASEL 14.2(2022):22.
|
修改评论