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

Abstract

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 vB 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.