Antiferromagnetic and spin gap phases of the anisotropic Kondo necklace model

TL;DR

This study investigates how anisotropies affect quantum phase transitions in the Kondo necklace model across different dimensions, revealing new behaviors and calculating critical points and order parameters.

Contribution

It introduces a comprehensive analysis of anisotropic effects on the Kondo necklace model using a bond operator mean field approach, highlighting novel phase transition behaviors.

Findings

Identification of critical ratios $(t/J)_c$ for quantum phase transitions.

Discovery of new behaviors for easy-axis anisotropy $ ext{delta} > 1$.

Calculation of antiferromagnetic order parameters in the ordered phase.

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 $t > t_c$.