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Integrability to chaos transition through Krylov approach for state evolution

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arxiv 2309.13427 v1 pith:O7WZ5PP2 submitted 2023-09-23 quant-ph

Gastón F. Scialchi , Augusto J. Roncaglia , Diego A. Wisniacki This is my paper · ORCID
classification quant-ph
keywords krylovchaosbasisdispersionquantumapproachcomplexityinitial
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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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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic Spread Complexity from Level Statistics: From Chaos to Integrability

    hep-th 2026-08 conditional novelty 7.0 of 10

    The finite-time peak of spread complexity is controlled by the Fourier transform of the nearest-neighbour energy-level spacing distribution.

  2. Krylov-Space Memory Cores

    hep-th 2026-07 conditional novelty 6.0 of 10

    Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.

  3. Black Hole States in Quantum Spin Chains

    hep-th 2025-12 conditional novelty 6.0 of 10

    An equal-weight superposition of all non-crossing singlet pairings in a Heisenberg chain shows logarithmic entanglement growth (c≈5.2) and near-infinite-temperature thermalization.

  4. Krylov Complexity in Mixed Phase Space

    hep-th 2024-12 conditional novelty 6.0 of 10

    The Krylov complexity peak height correlates with the Brody parameter in mixed-phase-space quantum systems, diminishing as the spectrum becomes Poissonian.

  5. Higher-Order Krylov State Complexity in Random Matrix Quenches

    hep-th 2024-12 conditional novelty 5.0 of 10

    Higher-order generalized spread complexities show a more pronounced pre-equilibration peak than standard spread complexity in random matrix quenches, quantifying chaos more sharply up to third order.

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