中国物理B ›› 2017, Vol. 26 ›› Issue (8): 80502-080502.doi: 10.1088/1674-1056/26/8/080502

• GENERAL • 上一篇    下一篇

Identifying the closeness of eigenstates in quantum many-body systems

Hai-bin Li(李海彬), Yang Yang(杨扬), Pei Wang(王沛), Xiao-guang Wang(王晓光)   

  1. 1 Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China;
    2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
    3 Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China
  • 收稿日期:2017-02-22 修回日期:2017-04-22 出版日期:2017-08-05 发布日期:2017-08-05
  • 通讯作者: Hai-bin Li E-mail:hbli@zjut.edu.cn
  • 基金资助:

    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY16A050004), the Fundamental Research Funds for the Central Universities, China (Grant No. 2017FZA3005), and the National Natural Science Foundation of China (Grant No. 11475146).

Identifying the closeness of eigenstates in quantum many-body systems

Hai-bin Li(李海彬)1, Yang Yang(杨扬)1, Pei Wang(王沛)1,2, Xiao-guang Wang(王晓光)3   

  1. 1 Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China;
    2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
    3 Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China
  • Received:2017-02-22 Revised:2017-04-22 Online:2017-08-05 Published:2017-08-05
  • Contact: Hai-bin Li E-mail:hbli@zjut.edu.cn
  • About author:0.1088/1674-1056/26/8/
  • Supported by:

    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY16A050004), the Fundamental Research Funds for the Central Universities, China (Grant No. 2017FZA3005), and the National Natural Science Foundation of China (Grant No. 11475146).

摘要:

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems.

关键词: quantum chaos, thermalization, fidelity

Abstract:

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems.

Key words: quantum chaos, thermalization, fidelity

中图分类号:  (Quantum statistical mechanics)

  • 05.30.-d
03.65.-w (Quantum mechanics) 05.45.Mt (Quantum chaos; semiclassical methods) 02.30.Ik (Integrable systems)