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Krylov Complexity in Quantum Field Theory

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arxiv 2204.02250 v4 pith:TEB3KENA submitted 2022-04-05 hep-th cond-mat.stat-mechgr-qchep-phquant-ph

Kiran Adhikari , Sayantan Choudhury , Abhishek Roy This is my paper · ORCID
classification hep-thcond-mat.stat-mechgr-qchep-phquant-ph
keywords complexitykrylovfieldtheorybasisequalsquantumvolume
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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.

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  1. Generalized Krylov Complexity

    hep-th 2025-07 conditional novelty 5.0 of 10

    The paper defines generalized Krylov complexity for multi-generator unitary evolutions, computes it for U(1)xU(1), a U(1)xU(1) subgroup of SO(10), and SU(2), and introduces a weighted version.

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