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The anisotropic Kondo necklace model in 2D and 3D is treated as a genuine model for magnetic to Kondo singlet quantum phase transitions in the heavy fermion (HF) compounds.
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.
To get accurate results on the gap exponent we have used the Green's function approach
including a hard core repulsion to find the low energy excitation spectrum of the model. We have studied the effect of both inter-site (delta) and local (Delta) anisotropies on the critical exponent of the excitation gap in the paramagnetic phase.
We have also compared our results with previous bond operator mean field calculations.
We have also extended the treatment to finite fields using a generalised bond operator representation including all triplet states. The variation of critical tc with magnetic field and the associated phase diagram is derived. The influence of anisotropies and the different g-factors for localised and itinerant spins on the field dependence of tc is also investigated. It is found that three different types of behaviour may appear: (i) Destruction of antiferromangetism and appearance of a singlet state above a critical field. (ii) The inverse behaviour, namely field induced antiferromagnetism out of the Kondo singlet phase. (iii) Reentrance behaviour of the Kondo singlet phase as function of field strength. Moreover, we have shown that for one-dimensional model 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. In addition, 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. (It is a collaboration with P. Thalmeier, H. Rezania and S. Mahmoudian) |
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