Zeno dynamics and Cooperative Shielding from long range interaction

We analyze both single particle transport
models with long range hopping and many-body systems with long range interaction.
First we discuss a paradigmatic one dimensional disordered model with both nearest-neighbor and $1/r^{\alpha}$ hopping amplitudes. Such a model is relevant for different physical systems and it can be directly implemented in ion traps, where $\alpha$ can be tuned from zero to a value larger than one.
In case of long range hopping, in the large system size limit, we show the existence of a subspace where the dynamics occurs as if long range hopping was absent or reduced to short range. We named such effect {\it Cooperative Shielding}.
Cooperative shielding strongly affects transport properties: while long range hopping is usually thought to destroy localization, strong signatures of localization can be found in the shielded subspace.
Next, many-body quantum spin-$1/2$ systems with long-range interaction, are discussed. Contrary to the common expectation that long-range interaction should always induce an instantaneous spread of information in the thermodynamic limit, the shielding effect may lead to a finite velocity of the propagation of information or even the entire freezing of the dynamics, even in absence of disorder. This shielding phenomenon can be related to the quantum Zeno effect, which refers to the freezing of the dynamics into invariant subspaces in a system under continuous measurement. Thus long-range interaction plays a role similar to a measuring apparatus.