] 3 0 Ju n 20 06 Antiferromagnetic and spin gap phases of the anisotropic Kondo necklace model

We have studied the effect of anisotropies on the quantum phase transition of the Kondo necklace model in dimensions D=1, 2 and 3. Both the anisotropy δ of the inter-site interaction term and anisotropy ∆ of the on-site Kondo interaction have been included. We use a bond operator method with constraints implemented in mean field approximation. Starting from the paramagnetic phase we determine the critical ratio (t/J)c of the quantum critical point and associated scaling exponents of the Kondo-singlet gap. We show that in the case of easy-axis type anisotropy δ > 1 a qualitatively new behavior in comparison to the conventional Kondo necklace model with (δ,∆)=(0,1) appears. We have also obtained the antiferromagnetic order parameter in the long range ordered phase for t > tc.