Krylov Complexity in Quantum Field Theory
arXiv:2204.02250 · doi:10.1016/j.nuclphysb.2023.116263
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.
arXiv comment11 pages, 2 figures, Updated version, Accepted for publication in Nuclear Physics B
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