Krylov Complexity in Lifshitz-type Dirac Field Theories

• URL: http://arxiv.org/abs/2506.08765v2
• Date: Wed, 11 Jun 2025 13:21:01 GMT
• Title: Krylov Complexity in Lifshitz-type Dirac Field Theories
• Authors: Hamid R. Imani, K. Babaei Velni, M. Reza Mohammadi Mozaffar,
• Abstract summary: We study Krylov complexity in Lifshitz-type Dirac field theories.<n>We analyze the growth and saturation behavior of Krylov complexity in different regimes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent z. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of Krylov complexity in different regimes. We incorporate a hard UV cutoff and investigate the effects of lattice discretization, revealing fundamental differences between continuum and lattice models. In the presence of a UV cutoff, Krylov complexity exhibits an initial exponential growth followed by a linear regime, with saturation values dictated by the cutoff scale. For the lattice model, we find a fundamental departure from the continuum case: due to the finite Krylov basis, Krylov complexity saturates rather than growing indefinitely. Our findings suggest that Lifshitz scaling influences operator growth and information spreading in quantum systems.

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