The study of non-equilibrium quantum many-body systems presents enduring challenges, as the typical statistical mechanics system for matter at equilibrium is not applicable to such systems. Leveraging engineered Hamiltonians, ultracold quantum gases can simulate a variety of spin-lattice models and provide a powerful and tunable many-body platform to study the out-of-equilibrium dynamics and critical dynamics across quantum phase transitions. In this talk, I will present energy-resolved spin correlation measurements in a weakly interacting Fermi gas, which behaves as a many-body spin lattice in energy space with effective long-range interactions, simulating a model of quantum magnetism. I will discuss how the system magnetization is linked to the localization or spread of spin correlations in energy landscape. The microscopic feature of spin correlation offers an important complement to macroscopic magnetization measurement, enhancing our understanding of the ferromagnetic phase transition. Therefore, we highlight energy-space correlation as an observable in the studies of transition between dynamical phases in quantum simulators accomplished by weakly interacting Fermi gases.