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Krylov complexity in quantum field theory, and beyond

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arxiv 2212.14429 v3 pith:KFDYJSOG submitted 2022-12-29 hep-th quant-ph

classification hep-thquant-ph
keywords complexitykrylovcoefficientsfieldlanczosmodelsquantumtheory
verification ladder T0 review T1 audit T2 compute T3 formal
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We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of Lanczos coefficients, which goes beyond previously observed universality. We confirm that in all cases the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss temperature dependence of Lanczos coefficients and note that the relation between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime governed by the physics at the UV cutoff. Contrary to previous suggestions, we show scenarios when Krylov complexity in quantum field theory behaves qualitatively differently from the holographic complexity.

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Cited by 8 Pith papers

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

  1. Holographic timelike complexity for de Sitter

    hep-th 2026-07 conditional novelty 6.0 of 10

    Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.

  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. Quantum Cosmology in Krylov Space: Complexity and Entropy

    gr-qc 2025-11 conditional novelty 6.0 of 10

    In a sharply peaked Gaussian state of a flat FLRW universe with a massless scalar clock, Krylov state complexity grows as σ²(φ−φ0)²/4 and operator complexity is exactly twice that, in both Wheeler-DeWitt and loop quan...

  4. Temperature dependence in Krylov space

    hep-th 2025-08 conditional novelty 6.0 of 10

    Temperature dependence of Lanczos coefficients is governed by two decoupled Toda chains, yielding a 'Krylov bootstrap' consistency criterion and exponentially small Krylov complexity at low temperature.

  5. 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 ...

  6. 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.

  7. Generalized Krylov Complexity

    hep-th 2025-07 conditional novelty 5.0 of 10

    The paper defines generalized Krylov complexity for multi-generator unitary evolutions, computes it for U(1)xU(1), a U(1)xU(1) subgroup of SO(10), and SU(2), and introduces a weighted version.

  8. Quantum complexity phase transition in fermionic quantum circuits

    quant-ph 2025-07 conditional novelty 5.0 of 10

    A measure of operator spreading, Krylov complexity, undergoes a phase transition in quantum percolation: at the percolation threshold for free fermions, but at a lower threshold p=1/4 for 1D interacting fermions.

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