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  • Letter
  • Open Access

Krylov complexity in mixed phase space

Kyoung-Bum Huh1, Hyun-Sik Jeong2, Leopoldo A. Pando Zayas3,4, and Juan F. Pedraza2

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Phys. Rev. D 111, L121902 – Published 16 June, 2025

DOI: https://doi.org/10.1103/gmy7-dn7l

Abstract

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.

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Information

Phys. Rev. D 111, L121902– Published 16 June, 2025
  • Received 14 February 2025
  • Accepted 21 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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