Krylov Complexity in Quantum Field Theory
High Energy Physics - Theory
2023-06-21 v4 Statistical Mechanics
General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2204.02250,
title = {Krylov Complexity in Quantum Field Theory},
author = {Kiran Adhikari and Sayantan Choudhury and Abhishek Roy},
journal= {arXiv preprint arXiv:2204.02250},
year = {2023}
}
Comments
11 pages, 2 figures, Updated version, Accepted for publication in Nuclear Physics B