Krylov complexity in quantum field theory, and beyond

TL;DR

This paper investigates Krylov complexity across various quantum field theory models, revealing new asymptotic behaviors, confirming bounds related to chaos, and highlighting differences from holographic complexity.

Contribution

It provides the first comprehensive analysis of Krylov complexity in diverse quantum field theories, uncovering new asymptotic behaviors and clarifying its relation to chaos and holographic complexity.

Findings

Asymptotic behavior of Lanczos coefficients beyond universality

Exponential growth of Krylov complexity satisfies a generalized chaos bound

Krylov complexity can behave differently from holographic complexity in QFT

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.