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Paper   IPM / Physic / 17339
School of Physics
  Title:   Krylov Complexity in Lifshitz-type Scalar Field Theories
1.  M.J. Vasli
2.  K. Babaei Velni
3.  M.R. Mohammdi Mozaffar
4.  A. Mollabashi
5.  M. Alishahiha
  Status:   Preprint
  Year:  2023
  Supported by:  IPM
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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