Freezing and Shielding under Global Quenches for Long-Range Interacting Many-Body Systems

We investigate the time evolution of a Fermi-Hubbard model with long range hopping following a sudden quench of the local interactions among different spin species. The quasi-particle spectrum consists of gapped low-energy levels while the high energy modes accumulate at a single point. When the low energy gaps are large enough, turning on the local interactions does not effectively mix high and low energy modes, leading to the freezing of the dynamical evolution. In general, the states within the excited subspace are shielded from the long-range signatures of the model, which are responsible for the low energy extended states, and the dynamics effectively look as if long-range hopping were absent. This cooperative shielding mechanism becomes evident in presence of disorder. It is shown that shielding and freezing are a universal feature of long-range interacting systems and conjecture that they are related to the existence of quasi-stationary states.