Entanglement in noncritical inhomogeneous quantum chains

We study an inhomogeneous critical Ising chain in a transverse field whose couplings decay exponentially from the center. In strong inhomogeneity limit, we apply Fisher's renormalization group to show that ground state is formed by concentric singlets similar those of rainbow XX model. weak map model massless Majorana fermion living hyperbolic space-time, where, using conformal theory techniques, derive entanglement entropy and it presents linear scaling. also noncritical for mapped massive fermion, while regime, exhibits trivial nontrivial topological phases separation between regions with high low entanglement. present Hamiltonian