Affiliation:
1. Shanghai Jiao Tong University
2. Instituto de Física Teórica UAM/CSIC
3. University of Michigan, Ann Arbor
4. The Abdus Salam International Centre for Theoretical Physics
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.
Published by the American Physical Society
2025
Funder
Ministerio de Economía y Competitividad
Comunidad de Madrid
Agencia Estatal de Investigación
Ministerio de Ciencia e Innovación
European Regional Development Fund
U.S. Department of Energy
Foreign Young Scholars Research Fund
Publisher
American Physical Society (APS)