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.
Krylov complexity remains nonsingular at SWSSB crossovers but shows a singular area-to-volume-law transition at genuine mixed-state SWSSB phase transitions in dephasing channels.
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
Derivative of Krylov spread complexity diverges logarithmically at SSH topological transitions and is bounded by fidelity susceptibility in general two-band Hamiltonians, with a non-unitary duality between phases.
citing papers explorer
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Krylov Winding and Emergent Coherence in Operator Growth Dynamics
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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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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Krylov Complexity and Mixed-State Phase Transition
Krylov complexity remains nonsingular at SWSSB crossovers but shows a singular area-to-volume-law transition at genuine mixed-state SWSSB phase transitions in dephasing channels.
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Krylov Complexity Under Hamiltonian Deformations and Toda Flows
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
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Krylov complexity and fidelity susceptibility in two-band Hamiltonians
Derivative of Krylov spread complexity diverges logarithmically at SSH topological transitions and is bounded by fidelity susceptibility in general two-band Hamiltonians, with a non-unitary duality between phases.
- Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity