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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
classification hep-thcond-mat.stat-mechquant-ph
keywords behaviorcoefficientsfinitekrylovlanczostheoriescomplexitydynamical
verification ladder T0 review T1 audit T2 compute T3 formal
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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 2 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. 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.

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