Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning

doi:10.1088/1674-1056/ad8cb9

中国物理B ›› 2025, Vol. 34 ›› Issue (1): 17103-017103.doi: 10.1088/1674-1056/ad8cb9

Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning

Bohan Zheng(郑博涵)^1,†, Siyu Zhu(朱思宇)^2,†, Xingping Zhou(周兴平)^2,‡, and Tong Liu(刘通)^3,§

1 School of Computer Science and Technology, School of Software, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
3 Department of Applied Physics, School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

收稿日期:2024-05-31 修回日期:2024-10-19 接受日期:2024-10-30 发布日期:2024-12-12
通讯作者: Xingping Zhou, Tong Liu E-mail:zxp@njupt.edu.cn;t6tong@njupt.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Nanjing University of Posts and Telecommunications (Grant Nos. NY223109, NY220119, and NY221055), China Postdoctoral Science Foundation (Grant No. 2022M721693), and the National Natural Science Foundation of China (Grant No. 12404365).

Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning

Bohan Zheng(郑博涵)^1,†, Siyu Zhu(朱思宇)^2,†, Xingping Zhou(周兴平)^2,‡, and Tong Liu(刘通)^3,§

1 School of Computer Science and Technology, School of Software, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
3 Department of Applied Physics, School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Received:2024-05-31 Revised:2024-10-19 Accepted:2024-10-30 Published:2024-12-12
Contact: Xingping Zhou, Tong Liu E-mail:zxp@njupt.edu.cn;t6tong@njupt.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Nanjing University of Posts and Telecommunications (Grant Nos. NY223109, NY220119, and NY221055), China Postdoctoral Science Foundation (Grant No. 2022M721693), and the National Natural Science Foundation of China (Grant No. 12404365).

摘要/Abstract

摘要： Classification of quantum phases is one of the most important areas of research in condensed matter physics. In this work, we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning. Firstly, we choose two advanced unsupervised learning algorithms, namely, density-based spatial clustering of applications with noise (DBSCAN) and ordering points to identify the clustering structure (OPTICS), to explore the distinct phases of the Aubry-André-Harper model and the quasiperiodic p-wave model. The unsupervised learning results match well with those obtained through traditional numerical diagonalization. Finally, we assess similarity across different algorithms and find that the highest degree of similarity between the results of unsupervised learning algorithms and those of traditional algorithms exceeds 98%. Our work sheds light on applications of unsupervised learning for phase classification.

关键词: quantum phase, quasiperiodic, machine learning

Abstract: Classification of quantum phases is one of the most important areas of research in condensed matter physics. In this work, we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning. Firstly, we choose two advanced unsupervised learning algorithms, namely, density-based spatial clustering of applications with noise (DBSCAN) and ordering points to identify the clustering structure (OPTICS), to explore the distinct phases of the Aubry-André-Harper model and the quasiperiodic p-wave model. The unsupervised learning results match well with those obtained through traditional numerical diagonalization. Finally, we assess similarity across different algorithms and find that the highest degree of similarity between the results of unsupervised learning algorithms and those of traditional algorithms exceeds 98%. Our work sheds light on applications of unsupervised learning for phase classification.

Key words: quantum phase, quasiperiodic, machine learning

中图分类号: (Quasicrystals)

71.23.Ft

71.10.Fd (Lattice fermion models (Hubbard model, etc.)) 71.23.An (Theories and models; localized states)

Bohan Zheng(郑博涵), Siyu Zhu(朱思宇), Xingping Zhou(周兴平), and Tong Liu(刘通). Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning[J]. 中国物理B, 2025, 34(1): 17103-017103.

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Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning

Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning

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