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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, Jc.
Moreover, our results show that the onset of anisotropy in the
XY term of the itinerant interactions develops the antiferromagnetic order for J < Jc.
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.
Moreover, the Kondo necklace model has been studied on the ladder geometry and different anisotropy in the interaction between the spin of conduction electrons. We have shown that the mean field approach predicts two different phases for the odd leg ladders while this method fails to work properly for the even leg ladders. We have also applied the spin wave theory for the two leg ladder and found no magnetic order can be assumed in this case for small local anisotropy (delta < 1). We have concluded that the ladders with even legs are always in the Kondo singlet phase. While for the odd leg ladders a quantum phase transition defines the border between the Kondo singlet and antiferromagnetic phases. Both types of ladders show a Kondo singlet to antiferromagnetic phase transition in the Ising limit, delta > 1. |
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