Related papers: Integrability to chaos transition through Krylov approach for state evolution

Integrability to chaos transition through Krylov approach for state evolution

URL: http://arxiv.org/abs/2309.13427v1
Date: Sat, 23 Sep 2023 16:35:19 GMT
Title: Integrability to chaos transition through Krylov approach for state evolution
Authors: Gast\'on F. Scialchi, Augusto J. Roncaglia and Diego A. Wisniacki
Abstract summary: complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion. This property assigns a central role to the Krylov basis in the investigation of quantum chaos.
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License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et al, Physical Review D 106, 046007 (2022)]. This property assigns a central role to the Krylov basis in the investigation of quantum chaos. Here, we delve into the transition from integrability to chaos using the Krylov approach, employing an Ising spin chain and a banded random matrix model as our testing models. Our findings indicate that both the saturation of Krylov complexity and the dispersion of the Lanczos coefficients can exhibit a significant dependence on the initial condition. However, both quantities can gauge dynamical quantum chaos with a proper choice of the initial state.

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