  We study the ground-state entanglement of one-dimensional harmonic chains
that are coupled to each other by a collective interaction as realized e.g. in
an anisotropic ion crystal. Due to the collective type of coupling, where each
chain interacts with every other one in the same way,the total system shows
critical behavior in the direction orthogonal to the chains while the isolated
harmonic chains can be gapped and non-critical. We derive lower and most
importantly upper bounds for the entanglement,quantified by the von Neumann
entropy, between a compact block of oscillators and its environment. For
sufficiently large size of the subsystems the bounds coincide and show that the
area law for entanglement is violated by a logarithmic correction.
