Krylov Complexity in Lifshitz-type Scalar Field Theories

• URL: http://arxiv.org/abs/2307.08307v2
• Date: Sun, 10 Mar 2024 16:40:30 GMT
• Title: Krylov Complexity in Lifshitz-type Scalar Field Theories
• Authors: M. J. Vasli, K. Babaei Velni, M. R. Mohammadi Mozaffar, A. Mollabashi, M. Alishahiha
• Abstract summary: We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar theories. We examine the effects of mass, finite ultraviolet cutoff, and finite lattice spacing on the behavior of the Lanczos coefficients. We find that our results are similar to those previously observed in the literature for relativistic theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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