Block entropy and quantum phase transition in the anisotropic Kondo necklace model

We study the von Neumann block entropy in the Kondo necklace model for different anisotropies eta in the XY interaction between conduction spins using the density matrix renormalization group method. It was found that the block entropy presents a maximum for each eta considered, and, comparing it with the results of the quantum criticality of the model based on the behavior of the energy gap, we observe that the maximum block entropy occurs at the quantum critical point between an antiferromagnetic and a Kondo singlet state, so this measure of entanglement is useful for giving information about where a quantum phase transition occurs in this model. We observe that the block entropy also presents a maximum at the quantum critical points that are obtained when an anisotropy Delta is included in the Kondo exchange between localized and conduction spins; when Delta diminishes for a fixed value of eta, the critical point increases, favoring the antiferromagnetic phase.