Abstract
We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in d-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the “staggering” of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.
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Acknowledgments
We thank the participants of the Asia Pacific Center for Theoretical Physics (APCTP) Focus Program “Holography 2022: quantum matter and spacetime” and “Integrability, duality and related topics” for valuable discussions on the subject. We are especially thankful to Anatoly Dymarsky for discussing his ongoing work on similar topics during the APCTP Focus Program “Holography 2022: quantum matter and spacetime” [73], which motivated us to consider the relevance of ultra-violet (UV) cutoffs in our studies. We are also grateful to Adolfo del Campo, Anatoly Dymarsky, Song He, Pratik Nandy and Horacio M. Pastawski for comments and suggestions on the first version of this manuscript. H. A. Camargo also thanks Luis Apolo, Pawel Caputa, Christian Ferko, Chen-Te Ma and Pratik Nandy for discussions and correspondence. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF- 2021R1A2C1006791), the AI-based GIST Research Scientist Project grant funded by the GIST in 2023. This work was also supported by Creation of the Quantum Information Science R&D Ecosystem (Grant No. 2022M3H3A106307411) through the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science and ICT). H. A. Camargo, V. Jahnke and M. Nishida were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2022R1I1A1A01070589, NRF-2020R1I1A1A01073135, NRF-2020R1I1A1A01072726) respectively.
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Camargo, H.A., Jahnke, V., Kim, KY. et al. Krylov complexity in free and interacting scalar field theories with bounded power spectrum. J. High Energ. Phys. 2023, 226 (2023). https://doi.org/10.1007/JHEP05(2023)226
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DOI: https://doi.org/10.1007/JHEP05(2023)226