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Krylov Complexity in Lifshitz-type Scalar Field Theories

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arxiv 2307.08307 v2 pith:G3DRNJLX submitted 2023-07-17 hep-th cond-mat.stat-mechquant-ph

M. J. Vasli , K. Babaei Velni , M. R. Mohammadi Mozaffar , A. Mollabashi , M. Alishahiha This is my paper · ORCID
classification hep-thcond-mat.stat-mechquant-ph
keywords behaviorcoefficientsfinitekrylovlanczostheoriescomplexitydynamical
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We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar theories, characterized by their integer dynamical exponent, at finite temperature. In this non-relativistic setup, we examine the effects of mass, finite ultraviolet cutoff, and finite lattice spacing on the behavior of the Lanczos coefficients. We also investigate the effect of the dynamical exponent on the asymptotic behavior of the Lanczos coefficients, which show a universal scaling behavior. We carefully examine how these results can affect different measures in Krylov space, including Krylov complexity and entropy. Remarkably, we find that our results are similar to those previously observed in the literature for relativistic theories.

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Cited by 6 Pith papers

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

  1. 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.

  2. 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.

  3. 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...

  4. 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.

  5. 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.

  6. 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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