Out-of-time-order correlators in the one-dimensional XY model

We study the behavior of information spreading in the XY model, using out-of-time-order correlators (OTOCs). The effects of anisotropic parameter γ and external magnetic field λ on OTOCs are studied in detail within thermodynamical limits. The universal form which characterizes the wavefront of information spreading still holds in the XY model. The butterfly speed v _B depends on (γ, λ). At a fixed location, the early-time evolution behavior of OTOCs agrees with the results of the Hausdorff–Baker–Campbell expansion. For long-time evolution, OTOCs with local operators decay as for power law t ⁻¹, but those with nonlocal operators show different and nontrivial power law behaviors. We also observe temperature dependence for OTOCs when (γ = 0, λ = 1). At low temperature, the OTOCs with nonlocal operators show divergence over time. (paper)