Field-induced quantum phase transition in the anisotropic Kondo necklace model

Abstract

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. The variation of the quantum critical point (QCP) with anisotropy parameters has been investigated previously in the zero field case [1]. Here we extend 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 gfactors 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.

Green’s function approach to quantum criticality in the anisotropic Kondo necklace model

“…The constraint on the bosonic excitations has been implemented with the help of a hard core boson term at every site instead of applying a global constraint by introducing a chemical potential in the mean field approach. 14,15 The comparison of quantum critical points ͑J Ќ / J͒ c ͑␦ =1͒ as a function of ⌬ in Table I shows that deviations of the Tables I and II. two methods are quite small, up to 10% at the most. They are somewhat larger for the complementary case ͑⌬ =1͒ as a function of ␦ ͑up to ϳ17%͒, especially when the isotropic case ␦ = 1 is approached.…”

“…After diagonalization of H 2 , the singlet amplitude s and the chemical potential are determined self-consistently as a function of J Ќ / J by minimizing the total energy. 14,15 This means that and s will be slowly varying functions of the control parameter J Ќ / J. On the other hand, the present Green's function approach corresponds to fixing these two parameters to ͑J Ќ / J͒-independent constants given by s = 1 and = ͑J Ќ / 4͒͑2+⌬͒ which correspond to the mean field values for J Ќ / J = 0.…”

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

“…10 Mean field theory has also been applied to study the effect of magnetic field on the Kondo-necklace model. 11 However, for D = 1, the mean field approach always shows a nonmagnetic Kondo singlet phase even in the presence of anisotropy in the easy axis term. 10 In the present work, we want to study the possible quantum phase transition in the D = 1 Kondo-necklace model under the assumption of the anisotropy in the XY interaction ͑͒ between the spin of itinerant electrons.…”

Green’s function approach to the thermodynamic properties of the anisotropic Kondo necklace model

“…We have implemented the bond operator formalism 15,16 which has been used before within mean-field approximation 17,18 to determine the quantum critical phase diagram. It should be noticed that the mean-field approach fails to predict the quantum phase transition in the anisotropic one-dimensional model.…”