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Krylov complexity in saddle-dominated scrambling

Bhattacharjee, B and Cao, X and Nandy, P and Pathak, T (2022) Krylov complexity in saddle-dominated scrambling. In: Journal of High Energy Physics, 2022 (5).

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Official URL: https://doi.org/10.1007/JHEP05(2022)174


In semi-classical systems, the exponential growth of the out-of-time-order correlator (OTOC) is believed to be the hallmark of quantum chaos. However, on several occasions, it has been argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space. In this work, we probe such an integrable system exhibiting saddle-dominated scrambling through Krylov complexity and the associated Lanczos coefficients. In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times. The linear growth arises entirely due to the saddle, which dominates other phase-space points even away from itself. Our results reveal that the exponential growth of Krylov complexity can be observed in integrable systems with saddle-dominated scrambling and thus need not be associated with the presence of chaos.

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 Author.
Keywords: Field Theories in Lower Dimensions; Holography and Condensed Matter Physics (AdS/CMT); Integrable Field Theories
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 16 Sep 2022 04:43
Last Modified: 16 Sep 2022 04:43
URI: https://eprints.iisc.ac.in/id/eprint/76503

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