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  Eigenstate Thermalization, Random Matrix Theory, and Behemoths

Khaymovich, I. M., Haque, M., & McClarty, P. A. (2019). Eigenstate Thermalization, Random Matrix Theory, and Behemoths. Physical Review Letters, 122(7): 070601. doi:10.1103/PhysRevLett.122.070601.

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Khaymovich, Ivan M.1, Author           
Haque, Masudul1, Author           
McClarty, Paul A.1, Author           
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1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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

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 Dates: 2019-02-192019-02-22
 Publication Status: Issued
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Title: Physical Review Letters
  Abbreviation : Phys. Rev. Lett.
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. : American Physical Society
Pages: - Volume / Issue: 122 (7) Sequence Number: 070601 Start / End Page: - Identifier: ISSN: 0031-9007
CoNE: https://pure.mpg.de/cone/journals/resource/954925433406_1