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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
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 3 Pith papers

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

  1. 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...

  2. 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 ...

  3. 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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