  Chaotic dynamics in quantum many-body systems scrambles local information so
that at late times it can no longer be accessed locally. This is reflected
quantitatively in the out-of-time-ordered correlator of local operators, which
is expected to decay to zero with time. However, for systems of finite size,
out-of-time-ordered correlators do not decay exactly to zero and in this paper
we show that the residual value can provide useful insights into the chaotic
dynamics. When energy is conserved, the late-time saturation value of the
out-of-time-ordered correlator of generic traceless local operators scales as
an inverse polynomial in the system size. This is in contrast to the inverse
exponential scaling expected for chaotic dynamics without energy conservation.
We provide both analytical arguments and numerical simulations to support this
conclusion.
