Related papers: Krylov complexity in quantum field theory, and beyond

Krylov complexity in quantum field theory, and beyond

URL: http://arxiv.org/abs/2212.14429v2
Date: Thu, 13 Jun 2024 18:59:53 GMT
Title: Krylov complexity in quantum field theory, and beyond
Authors: Alexander Avdoshkin, Anatoly Dymarsky, Michael Smolkin,
Abstract summary: We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
Score: 44.99833362998488
License: http://creativecommons.org/licenses/by/4.0/
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 the UV-cutoff. In certain cases we find asymptotic behavior of Lanczos coefficients, which goes beyond previously observed universality. We confirm that in all cases the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss temperature dependence of Lanczos coefficients and note that the relation between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime governed by the physics at the UV cutoff. Contrary to previous suggestions, we show scenarios when Krylov complexity in quantum field theory behaves qualitatively differently from the holographic complexity.

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