Field induced magnetic quantum critical behavior in the Kondo necklace model

The Kondo necklace model augmented by a Zeeman term, serves as a useful model for heavy fermion compounds in an applied magnetic field. The phase diagram and thermodynamic behavior for arbitrary dimensions d has been investigated previously in the zero field case [D. Reyes, M. Continentino, Phys. Rev. B 76 (2007) 075114. ]. Here we extend the treatment to finite fields using a generalized bond operator representation for the localized and conduction electrons spins. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. Two critical magnetic fields are found namely, a critical magnetic field called henceforth hc1 and a saturation field nominated hc2. Then three important regions can be investigated: (i) Kondo spin liquid state (KSL) at low fields h<hc1; (ii) destruction of KSL state at h≥hc1 and appearance of a antiferromagnetic state; and (iii) saturated paramagnetic region above the upper critical field hc2