Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum

TL;DR

This paper investigates Krylov complexity in scalar quantum field theories, analyzing how mass, interactions, and ultraviolet cutoffs influence operator growth and complexity behavior at finite temperature.

Contribution

It introduces the effects of mass, interactions, and UV cutoffs on Krylov complexity and Lanczos coefficients, revealing phenomena like staggering and altered growth rates.

Findings

Ultraviolet cutoffs induce staggering in Lanczos coefficients.

Mass and interactions decrease the exponential growth rate of Krylov complexity.

Transitions in asymptotic behavior of complexity are observed under various deformations.

Abstract

We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in $d$-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the "staggering" of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.