  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-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.
