Krylov Complexity in Mixed Phase Space

• URL: http://arxiv.org/abs/2412.04963v2
• Date: Thu, 13 Feb 2025 10:24:00 GMT
• Title: Krylov Complexity in Mixed Phase Space
• Authors: Kyoung-Bum Huh, Hyun-Sik Jeong, Leopoldo A. Pando Zayas, Juan F. Pedraza,
• Abstract summary: We show that Krylov complexity consistently emerges as a reliable marker of quantum chaos. Results establish Krylov complexity as a powerful diagnostic of quantum chaos.
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• 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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