Krylov Complexity in Quantum Field Theory

TL;DR

This paper investigates Krylov complexity in quantum field theory, revealing its relation to holographic complexity, and demonstrates its scaling with volume and connection to particle number, including studies of chaos in inverted oscillators.

Contribution

It introduces a formalism linking Krylov complexity with holographic complexity and explores its behavior in free scalar fields and chaotic systems.

Findings

Krylov complexity equals average particle number in certain settings

Complexity scales with volume in quantum field theory

Surprising similarities with holographic complexity observed

Abstract

In this paper, we study the Krylov complexity in quantum field theory and make a connection with the holographic "Complexity equals Volume" conjecture. When Krylov basis matches with Fock basis, for several interesting settings, we observe that the Krylov complexity equals the average particle number showing that complexity scales with volume. Using similar formalism, we compute the Krylov complexity for free scalar field theory and find surprising similarities with holography. We also extend this framework for field theory where an inverted oscillator appears naturally and explore its chaotic behavior.