Phase diagram of the one-dimensional anisotropic Kondo-necklace model

Abstract

The one-dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising-type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction $(J)$ between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value ${J}_{c}$. Moreover, our results show that the onset of anisotropy in the $XY$ term of the itinerant interactions develops the antiferromagnetic order for $Jl{J}_{c}$. This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic $XY$ interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.