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Long-range interactions exhibit surprising features which have been lessexplored so far. Here, studying a one-dimensional fermionic chain withlong-range hopping and pairing, we discuss some general features associated tothe presence of long-range entanglement. In particular, after determining thealgebraic decays of the correlation functions, we prove that a long-rangequantum mutual information exists if the exponent of the decay is not largerthan one. Moreover, we show that the time evolution triggered by a quantumquench between short-range and long-range regions, can be characterized bydynamical quantum phase transitions without crossing any phase boundary. Weshow, also, that the adiabatic dynamics is dictated by the divergence of atopological length scale at the quantum critical point, clarifying theviolation of the Kibble-Zurek mechanism for long-range systems.

Correlations, long-range entanglement and dynamics in long-range Kitaev chains