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Krylov complexity in large q and double-scaled SYK model

Bhattacharjee, B and Nandy, P and Pathak, T (2023) Krylov complexity in large q and double-scaled SYK model. In: Journal of High Energy Physics, 2023 (8).

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Official URL: https://doi.org/10.1007/JHEP08(2023)099


Considering the large q expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the t/q effects. The Krylov complexity naturally describes the “size” of the distribution while the higher cumulants encode richer information. We further consider the double-scaled limit of SYK q at infinite temperature, where q ~ N . In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge. The growth of Krylov complexity appears to be “hyperfast”, which is previously conjectured to be associated with scrambling in de Sitter space. © 2023, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 07 Nov 2023 04:34
Last Modified: 07 Nov 2023 04:34
URI: https://eprints.iisc.ac.in/id/eprint/83055

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