  This article introduces and discusses the concept of entanglement detachment.
Under some circumstances, enlarging a few couplings of a Hamiltonian can
effectively detach a (possibly disjoint) block within the ground state. This
detachment is characterized by a sharp decrease in the entanglement entropy
between block and environment, and leads to an increase of the internal
correlations between the (possibly distant) sites of the block. We provide some
examples of this detachment in free fermionic systems. The first example is an
edge-dimerized chain, where the second and penultimate hoppings are increased.
In that case, the two extreme sites constitute a block which disentangles from
the rest of the chain. Further examples are given by (a) a superlattice which
can be detached from a 1D chain, and (b) a star-graph, where the extreme sites
can be detached or not depending on the presence of an external magnetic field,
in analogy with the Aharonov-Bohm effect. We characterize these detached blocks
by their reduced matrices, specially through their entanglement spectrum and
entanglement Hamiltonian.
