The 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 a 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 $0\le \gamma \le 1$, 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 space-time, 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 $\gamma ⟷1-\gamma$, whose fixed point $\gamma =1/2$ corresponds to the usual rainbow model. Finally, we study the robustness of nontrivial topological phases in the presence of the defect.

• Received 7 January 2020
• Revised 21 April 2020
• Accepted 27 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.205121