Extensive limit of a non-extensive entanglement entropy

An important calculation has been that of the (von Neumann) entanglement entropy of the ground state of 1-dimensional lattice models at criticality and of their massive perturbations. This entropy turned out to be, generally, non-extensive. It was noticed, by contrast, that the Tsallis entropy of such systems can be extensive for a particular value of the non-extensive parameter. This value was expressed as function of the central charge of the underlying conformal field theory. We provide an answer to the question on why for central charge approaching infinity, extensivity of the von Neumann entropy of the ground state is restored.