  The {\em rainbow state} denotes a set of valence bond states organized
concentrically around the center of a spin 1/2 chain. It is the ground state of
an inhomogeneous XX Hamiltonian and presents maximal violation of the area law
of entanglement entropy. Here, we add a tunable exchange coupling constant at
the center, $\gamma$, and show that it induces entanglement transitions of the
ground state. At very strong inhomogeneity, the rainbow state survives for $0
\leq \gamma \leq 1$, while outside that region the ground state is a product of
dimers. In the weak inhomogeneity regime the entanglement entropy satisfies a
volume law, derived from CFT in curved spacetime, with an effective central
charge that depends on the inhomogeneity parameter and $\gamma$. In all regimes
we have found that the entanglement properties are invariant under the
transformation $\gamma \longleftrightarrow 1 - \gamma$, whose fixed point
$\gamma = \frac{1}{2}$ corresponds to the usual rainbow model. Finally, we
study the robustness of non trivial topological phases in the presence of the
defect.
