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Chin. Phys. B, 2017, Vol. 26(8): 080502    DOI: 10.1088/1674-1056/26/8/080502
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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 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

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.

Keywords:  quantum chaos      thermalization      fidelity  
Received:  22 February 2017      Revised:  22 April 2017      Accepted manuscript online: 
PACS:  05.30.-d (Quantum statistical mechanics)  
  03.65.-w (Quantum mechanics)  
  05.45.Mt (Quantum chaos; semiclassical methods)  
  02.30.Ik (Integrable systems)  

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).

Corresponding Authors:  Hai-bin Li     E-mail:
About author:  0.1088/1674-1056/26/8/

Cite this article: 

Hai-bin Li(李海彬), Yang Yang(杨扬), Pei Wang(王沛), Xiao-guang Wang(王晓光) Identifying the closeness of eigenstates in quantum many-body systems 2017 Chin. Phys. B 26 080502

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