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

Abstract

We have studied the two-dimensional anisotropic Kondo necklace model with antiferromagnetic (AF) Kondo coupling ${J}_{\ensuremath{\perp}}$ and exchange coupling between ``itinerant'' spins $J$ on the square lattice. The bond operator formalism is used to transform the spin model to a hard-core bosonic gas. We have used the Green's function approach to obtain the temperature dependence of spin excitation spectrum (triplet gap). We have also found the temperature dependence of the specific heat and the local spin-correlation function between localized and itinerant spins for various Kondo couplings ${J}_{\ensuremath{\perp}}/J$ and anisotropies in both coupling strengths. Furthermore we studied the temperature dependence of the structure factor for localized spins which is determined by effective interactions via itinerant spins. For low temperature and close to the quantum critical point we have obtained an analytical formula for temperature dependence of the energy gap and specific heat. Finally we compared our results with those of previous mean-field treatments.