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    Eigenstate Thermalization, Random Matrix Theory and Behemoths


    Khaymovich, Ivan M. and Haque, Masud and McClarty, Paul A. (2018) Eigenstate Thermalization, Random Matrix Theory and Behemoths. Working Paper. arXiv.

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    Abstract

    The eigenstate thermalization hypothesis (ETH) is one of the cornerstones in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this paper. We report on the construction of highly nonlocal operators, Behemoths, that are building blocks for various kinds of local and non-local operators. The Behemoths have a singular distribution and width w∼D−1 (D being the Hilbert space dimension). From them, one may construct local operators with the ordinary Gaussian distribution and w∼D−1/2 in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with w∼D−δ, 0<δ<1/2. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of non-integrable many-body systems.

    Item Type: Monograph (Working Paper)
    Keywords: Eigenstate Thermalization; Random Matrix Theory; quantum statistical mechanics;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10556
    Identification Number: arxiv.org/abs/1806.09631
    Depositing User: Masud Haque
    Date Deposited: 21 Feb 2019 16:36
    Publisher: arXiv
    URI:

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