  Long-range interactions exhibit surprising features which have been less
explored so far. Here, studying a one-dimensional fermionic chain with
long-range hopping and pairing, we discuss some general features associated to
the presence of long-range entanglement. In particular, after determining the
algebraic decays of the correlation functions, we prove that a long-range
quantum mutual information exists if the exponent of the decay is not larger
than one. Moreover, we show that the time evolution triggered by a quantum
quench between short-range and long-range regions, can be characterized by
dynamical quantum phase transitions without crossing any phase boundary. We
show, also, that the adiabatic dynamics is dictated by the divergence of a
topological length scale at the quantum critical point, clarifying the
violation of the Kibble-Zurek mechanism for long-range systems.
