  Thanks to their prominent collective character, long-range interactions
promote information spreading and generate forms of entanglement scaling, which
cannot be observed in traditional systems with local interactions. In this
work, we study the asymptotic behavior of the entanglement entropy for Kitaev
chains with long-range hopping and pairing couplings decaying with a power law
of the distance. We provide a fully-fledged analytical and numerical
characterization of the asymptotic growth of the ground state entanglement in
the large subsystem size limit, finding that the truly non-local nature of the
model leads to an extremely rich phenomenology. Most significantly, in the
strong long-range regime, we discovered that the system ground state may have a
logarithmic, fractal, or volume-law entanglement scaling, depending on the
value of the chemical potential and on the strength of the power law decay.
