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Building upon recent research in spin systems with non-local interactions,this study investigates operator growth using the Krylov complexity indifferent non-local versions of the Ising model. We find that the non-localityresults in a faster scrambling of the operator to all sites. While thesaturation value of Krylov complexity of local integrable and local chaotictheories differ by a significant margin, this difference is much suppressedwhen non-local terms are introduced in both regimes. This results from thefaster scrambling of information in the presence of non-locality. In addition,we investigate the behavior of level statistics and spectral form factor asprobes of quantum chaos to study the integrability breaking due to non-localinteractions. Our numerics indicate that even in the non-local case, Krylovcomplexity can distinguish between different underlying theories as well asdifferent degrees of non-locality.

Krylov complexity for non-local spin chains