Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin- 12 XYZ chains

Out-of-time-ordered correlators (OTOCs) help characterize the scrambling of quantum information and are usually studied in the context of nonintegrable systems. In this work, we compare the relaxation dynamics of OTOCs in interacting integrable and nonintegrable spin-$\frac{1}{2}$ XYZ chains in regimes without a classical counterpart. In both kinds of chains, using the presence of symmetries such as $U(1)$ and supersymmetry, we consider regimes in which the OTOC operators overlap or not with the Hamiltonian. We show that the relaxation of the OTOCs is slow (fast) when there is (there is not) an overlap, independently of whether the chain is integrable or nonintegrable. When slow, we show that the OTOC dynamics follows closely that of the two-point correlators. We study the dynamics of OTOCs using numerical calculations, and gain analytical insights from the properties of the diagonal and of the off-diagonal matrix elements of the corresponding local operators in the energy eigenbasis.