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Krylov complexity in quantum field theory, and beyond

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arxiv 2212.14429 v3 pith:KFDYJSOG submitted 2022-12-29 hep-th quant-ph

Krylov complexity in quantum field theory, and beyond

classification hep-th quant-ph
keywords complexitykrylovcoefficientsfieldlanczosmodelsquantumtheory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of Lanczos coefficients, which goes beyond previously observed universality. We confirm that in all cases the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss temperature dependence of Lanczos coefficients and note that the relation between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime governed by the physics at the UV cutoff. Contrary to previous suggestions, we show scenarios when Krylov complexity in quantum field theory behaves qualitatively differently from the holographic complexity.

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Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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  10. The Information Content of Krylov Observables: A Machine Learning Approach

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