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    Statistical properties of eigenstate amplitudes in complex quantum systems


    Beugeling, Wouter and Bäcker, Arnd and Moessner, Roderich and Haque, Masud (2018) Statistical properties of eigenstate amplitudes in complex quantum systems. Physical Review E, 98 (022204). ISSN 1539-3755

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    Abstract

    We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wave-function amplitudes in a real-space basis. For single-particle “quantum billiards,” these real-space amplitudes are known to have Gaussian distribution for chaotic systems. In this work, we formulate and address the corresponding question for many-body lattice quantum systems. For integrable many-body systems, we examine the deviation from Gaussianity and provide evidence that the distribution generically tends toward power-law behavior in the limit of large sizes. We relate the deviation from Gaussianity to the entanglement content of many-body eigenstates. For integrable billiards, we find several cases where the distribution has power-law tails.

    Item Type: Article
    Keywords: Eigenstate thermalization; Quantum chaos; 1-dimensional spin chains; Quantum billiards; Bose-Hubbard model; Exact diagonalization;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10558
    Identification Number: https://doi.org/10.1103/PhysRevE.98.022204
    Depositing User: Masud Haque
    Date Deposited: 21 Feb 2019 16:59
    Journal or Publication Title: Physical Review E
    Publisher: American Physical Society
    Refereed: Yes
    URI:

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