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Spread complexity and quantum chaos for periodically driven spin chains

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arxiv 2405.16182 v2 pith:5Y2YVFBH submitted 2024-05-25 quant-ph cond-mat.stat-mechhep-thnlin.CD

Amin A. Nizami , Ankit W. Shrestha This is my paper · ORCID
classification quant-phcond-mat.stat-mechhep-thnlin.CD
keywords complexityspreadquantumarnoldichaoticbasisbehaviourchaos
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The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a pre-defined basis. It is known that this complexity is minimised by choosing the Krylov basis, thus defining the spread complexity. We study the dynamics of spread complexity for quantum maps using the Arnoldi iterative procedure. The main illustrative quantum many-body model we use is the periodically kicked Ising spin-chain with non-integrable deformations, a chaotic system where we look at both local and non-local interactions. In the various cases we find distinctive behaviour of the Arnoldi coefficients and spread complexity for regular vs. chaotic dynamics: suppressed fluctuations in the Arnoldi coefficients as well as larger saturation value in spread complexity in the chaotic case. We compare the behaviour of the Krylov measures with that of standard spectral diagnostics of chaos. We also study the effect of changing the driving frequency on the complexity saturation.

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Cited by 3 Pith papers

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

  1. Streamlined Krylov construction and classification of ergodic Floquet systems

    quant-ph 2024-12 conditional novelty 7.0 of 10

    A Szegő/CMV Krylov construction maps Floquet unitary dynamics to a five-diagonal chain, with a conjectured classification of chaos and integrability by Verblunsky coefficient asymptotics.

  2. Quantum chaos and pole skipping in two-dimensional conformal perturbation theory

    hep-th 2025-09 conditional novelty 6.0 of 10

    A deformed 2D CFT's stress-tensor pole-skipping point shifts at O(lambda^2); at h=1/2 the shift matches the holographic butterfly velocity.

  3. Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information

    quant-ph 2025-02 conditional novelty 5.0 of 10

    Time-averaged quantum Fisher information in Krylov space changes slope at the PT transition (gamma=1) and saturates near the entanglement transition (gamma=2) in the monitored SSH model, suggesting it as a probe of both.

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