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Title: Krylov complexity in quantum field theory, and beyond
A<sc>bstract</sc> 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.  more » « less
Award ID(s):
2013812
PAR ID:
10521429
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer (Journal of High Energy Physics)
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2024
Issue:
6
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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