Abstract
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with a UV-cutoff. In certain cases, we observe asymptotic behavior in Lanczos coefficients that extends beyond the previously observed universality. We confirm that, in all cases, the exponential growth of Krylov complexity satisfies the conjectured inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss the temperature dependence of Lanczos coefficients and note that the relationship between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime, governed by physics at the UV cutoff. Contrary to previous suggestions, we demonstrate scenarios in which Krylov complexity in quantum field theory behaves qualitatively differently from holographic complexity.
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Acknowledgments
We thank Dmitri Trunin for collaboration at the early stages of this project, and Luca Delacretaz, Matthew Dodelson, Oleg Lychkovskiy, Julian Sonner, Subir Sachdev, Adrian Sanchez-Garrido, and Erez Urbach for discussions. AA acknowledges support from a Kavli ENSI fellowship and the NSF under grant number DMR-1918065. AD is supported by the National Science Foundation under Grants PHY-2013812 and 2310426.
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Avdoshkin, A., Dymarsky, A. & Smolkin, M. Krylov complexity in quantum field theory, and beyond. J. High Energ. Phys. 2024, 66 (2024). https://doi.org/10.1007/JHEP06(2024)066
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DOI: https://doi.org/10.1007/JHEP06(2024)066