Krylov winding emerges as a generic feature of quantum chaotic systems from the universal operator growth bound, producing size winding when a low-rank Krylov-to-size mapping exists and the chaos bound saturates.
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Growth quenches are mapped to operator growth via the Krylov method, yielding a conjecture of linear Lanczos coefficients, localization criteria in Krylov and Fock space, a Lyapunov-exponent bound, and explicit realizations in SYK-inspired and East-West models.
In the quadratic resonant level model, Lanczos coefficients of impurity operators can be tuned to arbitrary growth patterns via coupling choice, showing they do not reliably indicate integrability or chaos.
citing papers explorer
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Quantum Quenches that Resemble Operator Growth
Growth quenches are mapped to operator growth via the Krylov method, yielding a conjecture of linear Lanczos coefficients, localization criteria in Krylov and Fock space, a Lyapunov-exponent bound, and explicit realizations in SYK-inspired and East-West models.
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Resonant level model from a Krylov perspective: Lanczos coefficients in a quadratic model
In the quadratic resonant level model, Lanczos coefficients of impurity operators can be tuned to arbitrary growth patterns via coupling choice, showing they do not reliably indicate integrability or chaos.