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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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.
Time-integrated spread complexity from bootstrapped Hamiltonian ensembles distinguishes ergodic regimes and shows a monotonic inverse relation to integrated fidelity decay in maximally entangled states.
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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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.
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Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity
Time-integrated spread complexity from bootstrapped Hamiltonian ensembles distinguishes ergodic regimes and shows a monotonic inverse relation to integrated fidelity decay in maximally entangled states.