Krylov complexity for nonlocal spin chains

Building upon recent research in spin systems with nonlocal interactions, this study investigates operator growth using the Krylov complexity in different nonlocal versions of the Ising model. We find that the nonlocality results in a faster scrambling of the operator to all sites. While the saturation value of Krylov complexity of local integrable and local chaotic theories differ by a significant margin, this difference is much suppressed when nonlocal terms are introduced in both regimes. This results from the faster scrambling of information in the presence of nonlocality. In addition, we investigate the behavior of level statistics and spectral form factor as probes of quantum chaos to study the integrability breaking due to nonlocal interactions. Our numerics indicate that in the nonlocal case, late time saturation of Krylov complexity distinguishes between different underlying theories, while the early time complexity growth distinguishes different degrees of nonlocality.