Quantum phase transitions with eigen microstate approach in one-dimensional transverse-field Ising model

doi:10.1088/1674-1056/add1c0

中国物理B ›› 2025, Vol. 34 ›› Issue (8): 86401-086401.doi: 10.1088/1674-1056/add1c0

Quantum phase transitions with eigen microstate approach in one-dimensional transverse-field Ising model

Zhongshan Su(苏中山)¹, Yuan Jiang(江源)¹, Gaoke Hu(胡高科)^2,1, Yue-Hua Su(苏跃华)³, Liangsheng Li(李粮生)⁴, Wen-Long You(尤文龙)^2,†, Maoxin Liu(刘卯鑫)^1,‡, and Xiaosong Chen(陈晓松)^1,§

1 School of Systems Science & Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China;
2 College of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
3 Department of Physics, Yantai University, Yantai 264005, China;
4 National Key Laboratory of Scattering and Radiation, Beijing 100854, China

收稿日期:2025-03-29 修回日期:2025-04-28 接受日期:2025-04-29 出版日期:2025-07-17 发布日期:2025-08-12
通讯作者: Wen-Long You, Maoxin Liu, Xiaosong Chen E-mail:wlyou@nuaa.edu.cn;mxliu@bnu.edu.cn;chenxs@bnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12475033, 12135003, 12174194, and 12405032) and the National Key Research and Development Program of China (Grant No. 2023YFE0109000). Maoxin Liu is supported by the Fundamental Research Funds for the Central Universities. Gaoke Hu acknowledges financial support from the China Postdoctoral Science Foundation (Grant No. 2023M730299).

Quantum phase transitions with eigen microstate approach in one-dimensional transverse-field Ising model

1 School of Systems Science & Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China;
2 College of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
3 Department of Physics, Yantai University, Yantai 264005, China;
4 National Key Laboratory of Scattering and Radiation, Beijing 100854, China

Received:2025-03-29 Revised:2025-04-28 Accepted:2025-04-29 Online:2025-07-17 Published:2025-08-12
Contact: Wen-Long You, Maoxin Liu, Xiaosong Chen E-mail:wlyou@nuaa.edu.cn;mxliu@bnu.edu.cn;chenxs@bnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12475033, 12135003, 12174194, and 12405032) and the National Key Research and Development Program of China (Grant No. 2023YFE0109000). Maoxin Liu is supported by the Fundamental Research Funds for the Central Universities. Gaoke Hu acknowledges financial support from the China Postdoctoral Science Foundation (Grant No. 2023M730299).

摘要/Abstract

摘要： We propose an eigen microstate approach (EMA) for analyzing quantum phase transitions in quantum many-body systems, introducing a novel framework that does not require prior knowledge of an order parameter. Using the transverse-field Ising model (TFIM) as a case study, we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates. Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition, as reflected in the behavior of specific components $\xi^{(k)}_i$ within the eigen microstates. This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.

关键词: eigen microstate approach, quantum phase transition, transverse-field Ising model

Abstract: We propose an eigen microstate approach (EMA) for analyzing quantum phase transitions in quantum many-body systems, introducing a novel framework that does not require prior knowledge of an order parameter. Using the transverse-field Ising model (TFIM) as a case study, we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates. Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition, as reflected in the behavior of specific components $\xi^{(k)}_i$ within the eigen microstates. This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.

Key words: eigen microstate approach, quantum phase transition, transverse-field Ising model

中图分类号: (Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.))

64.60.De

05.30.Rt (Quantum phase transitions) 75.40.Mg (Numerical simulation studies) 89.75.Da (Systems obeying scaling laws)

Zhongshan Su(苏中山), Yuan Jiang(江源), Gaoke Hu(胡高科), Yue-Hua Su(苏跃华), Liangsheng Li(李粮生), Wen-Long You(尤文龙), Maoxin Liu(刘卯鑫), and Xiaosong Chen(陈晓松). Quantum phase transitions with eigen microstate approach in one-dimensional transverse-field Ising model[J]. 中国物理B, 2025, 34(8): 86401-086401.

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Quantum phase transitions with eigen microstate approach in one-dimensional transverse-field Ising model

Quantum phase transitions with eigen microstate approach in one-dimensional transverse-field Ising model

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