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Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum

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arxiv 2212.14702 v4 pith:NE6U2CGN submitted 2022-12-30 hep-th cond-mat.stat-mechquant-ph

Hugo A. Camargo , Viktor Jahnke , Keun-Young Kim , Mitsuhiro Nishida This is my paper · ORCID
classification hep-thcond-mat.stat-mechquant-ph
keywords theoriescomplexitykrylovbehaviorcontinuouscutoffseffectsfield
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abstract

We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in $d$-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the "staggering" of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.

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Cited by 12 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. Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity

    hep-th 2024-12 conditional novelty 6.0 of 10

    In the brickwall model of a BTZ black hole, hand-tuned Gaussian randomness at a stretched horizon reproduces random-matrix-theory spectral statistics and Krylov complexity peaks for scalar and fermionic probes.

  5. Spread complexity for the planar limit of holography

    hep-th 2024-12 reject novelty 6.0 of 10

    Spread complexity is generalized to fermionic and supercoherent states, and applied to large-charge rotating strings in AdS5 x S5, yielding Krylov paths that reduce to effective SU(2)/SL(2) coherent-state complexity.

  6. Krylov Complexity in the Schr\"odinger Field Theory

    hep-th 2024-11 reject novelty 6.0 of 10

    For bosonic and fermionic Schrödinger fields with chemical potential μ≤0, the Lanczos coefficients grow linearly and the Krylov complexity grows exponentially with an extracted rate near 2.75/β, below the 4/β slope pr...

  7. 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.

  8. 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.

  9. 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.

  10. Higher-Order Krylov State Complexity in Random Matrix Quenches

    hep-th 2024-12 conditional novelty 5.0 of 10

    Higher-order generalized spread complexities show a more pronounced pre-equilibration peak than standard spread complexity in random matrix quenches, quantifying chaos more sharply up to third order.

  11. Statistics and Complexity of Wavefunction Spreading in Quantum Dynamical Systems

    quant-ph 2024-11 conditional novelty 5.0 of 10

    The moments of the spreading-operator measurement distribution are generalized spread complexities, which for GUE Hamiltonians peak more sharply at higher order and obey a norm bound.

  12. Revisit the relationship between spread complexity rate and radial momentum

    hep-th 2024-11 conditional novelty 3.0 of 10

    The paper shows that two proposed bulk momentum and boundary spread complexity correspondences are consistent, and that the match extends to any particle mass in AdS3.

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