Antiferromagnetic and spin gap phases of the anisotropic Kondo necklace model

Abstract

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 $\delta$ of the inter-site interaction term and anisotropy $\Delta$ 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 $\delta >1$ a qualitatively new behavior in comparison to the conventional Kondo necklace model with ($\delta$,$\Delta$)=(0,1) appears. We have also obtained the antiferromagnetic order parameter in the long range ordered phase for $t > t_c$.