Krylov complexity in quantum field theory, and beyond

A bstract 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 pre...

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Bibliographic Details
Published in:The journal of high energy physics Vol. 2024; no. 6; pp. 66 - 29
Main Authors: Avdoshkin, Alexander, Dymarsky, Anatoly, Smolkin, Michael
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 12.06.2024
Springer Nature B.V
SpringerOpen
Subjects:
AdS-CFT Correspondence
Asymptotic properties
Bosons
Classical and Quantum Gravitation
Coefficients
Complexity
Effective Field Theories
Elementary Particles
Fermions
Holography
Hypotheses
Inequality
Nonperturbative Effects
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Temperature dependence
AdS-CFT Correspondence
Effective Field Theories
Nonperturbative Effects
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract 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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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP06(2024)066