  Weakly interacting Fermi gases simulate spin-lattices in energy-space,
offering a rich platform for investigating information spreading and spin
coherence in a large many-body quantum system. We show that the collective spin
vector can be determined as a function of energy from the measured spin
density, enabling general energy-space resolved protocols. We measure an
out-of-time-order correlation function in this system and observe the energy
dependence of the many-body coherence.
