  We study the ground state entanglement entropy of the quantum Dyson
hierarchical spin chain in which the interaction decays algebraically with the
distance as $r^{-1-\sigma}$. We exploit the real-space renormalisation group
solution which gives the ground-state wave function in the form of a tree
tensor network and provides a manageable recursive expression for the reduced
density matrix of the renormalised ground state. Surprisingly, we find that at
criticality the entanglement entropy obeys an area law, as opposite to the
logarithmic scaling of short-range critical systems and of other
non-hierarchical long-range models. We provide also some analytical results in
the limit of large and small $\sigma$ that are tested against the numerical
solution of the recursive equations.

Statistical Mechanics;Quantum Physics