https://doi.org/10.1140/epjc/s10052-024-12609-9
Regular Article - Theoretical Physics
Krylov complexity in Lifshitz-type scalar field theories
1
Department of Physics, University of Guilan, P.O. Box 41335-1914, Rasht, Iran
2
Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, 606-8502, Kyoto, Japan
3
School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran
Received:
1
October
2023
Accepted:
23
February
2024
Published online:
7
March
2024
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.
© The Author(s) 2024
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