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Toda chain flow in Krylov space

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arxiv 1912.12227 v1 pith:Q24SHC6L submitted 2019-12-27 cond-mat.stat-mech hep-thmath-phmath.MPquant-ph

Anatoly Dymarsky , Alexander Gorsky This is my paper · ORCID
classification cond-mat.stat-mechhep-thmath-phmath.MPquant-ph
keywords imaginarykrylovspacetodaalonganalyticallyaxisbehavior
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We show in full generality that time-correlation function of a physical observable analytically continued to imaginary time is a tau-function of integrable Toda hierarchy. Using this relation we show that the singularity along the imaginary axis, which is a generic behavior for quantum non-integrable many-body system, is due to delocalization in Krylov space.

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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. 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. Operator K-complexity in DSSYK: Krylov complexity equals bulk length

    hep-th 2024-12 conditional novelty 6.0 of 10

    In the semiclassical limit of double-scaled SYK, Krylov complexity of an operator insertion equals total chord number, i.e., bulk wormhole length.

  3. Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

    quant-ph 2026-08 conditional novelty 5.0 of 10

    For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berr...

  4. 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 ...

  5. Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity

    hep-th 2026-02 conditional novelty 5.0 of 10

    Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.

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