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Krylov Localization and suppression of complexity

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arxiv 2112.12128 v2 pith:MYQJ2D6T submitted 2021-12-22 hep-th cond-mat.str-elquant-ph

E. Rabinovici , A. Sánchez-Garrido , R. Shir , J. Sonner This is my paper
classification hep-thcond-mat.str-elquant-ph
keywords complexityintegrablekrylovlocalizationmodelbehaviorchaoticdisorder
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Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones. In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems. We associate this behavior with a novel localization phenomenon on the Krylov chain by mapping the theory of complexity growth and spread to an Anderson localization hopping model with off-diagonal disorder, and find that localization is enhanced in the integrable case due to a stronger disorder in the hopping amplitudes, inducing an effective suppression of Krylov complexity. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain, and show that the same behavior results from a phenomenological model that we define: This model captures the essential features of our analysis and is able to reproduce the behaviors we observe for chaotic and integrable systems via an adjustable disorder parameter.

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Cited by 4 Pith papers

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

  1. 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.

  2. Krylov Complexity of Supersymmetric SYK Models

    hep-th 2025-11 conditional novelty 6.0 of 10

    In finite-size N=2 SYK, breaking supersymmetry with an irrelevant deformation pushes late-time Krylov complexity to roughly half the maximal Krylov-space bound, while a mass deformation leaves saturation complexity a ...

  3. The Information Content of Krylov Observables: A Machine Learning Approach

    hep-th 2026-07 conditional novelty 5.0 of 10

    Under chaos, the normalized Wigner negativity χ(t) carries information about the fine return dynamics that spread complexity C(t) cannot, with the asymmetry gap rising from +0.33 to +0.77 across the integrable-to-GUE ...

  4. Quasinormal modes and complexity in saddle-dominated SU(N) spin systems

    hep-th 2025-06 conditional novelty 5.0 of 10

    A family of SU(2) and SU(3) Lipkin-Meshkov-Glick-type Hamiltonians reproduces de Sitter quasinormal-mode densities of states, and late-time probes reveal integrability beneath saddle-dominated scrambling.

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