Phase diagram of the Kondo necklace model with planar and local anisotropies

We use the density matrix renormalization group to study the quantum critical behavior of a one-dimensional Kondo necklace model with two anisotropies: η in the XY interaction of conduction spins and Δ in the local exchange between localized and conduction spins (characterized by J). To do so, we calculate the gap between the ground and the first excited state for different values of η and Δ as a function of J, and fit it to a Kosterlitz-Thouless tendency; the point in which the gap vanishes is the quantum critical point Jc. To support our results, we calculate correlation functions and structure factors near the obtained critical points. The use of entanglement measures, specifically the von Neumann block entropy, to identify the quantum phase transition is also presented. Then we build the phase diagram of the model: for every Δ considered, any value of η > 0 generates a quantum phase transition from a Kondo singlet to an antiferromagnetic state at a finite value of J, and as η diminishes, so does Jc; when Δ diminishes for a fixed η, Jc increases, favoring the antiferromagnetic state