Kondo spin liquid and magnetically long-range ordered states in the Kondo necklace model

A simplified version of the symmetric Kondo lattice model, the Kondo necklace model, is studied by using a representation of impurity and conduction electron spins in terms of local Kondo singlet and triplet operators. Within a mean-field theory, a spin gap always appears in the spin triplet excitation spectrum in one dimension (1D), leading to a Kondo spin liquid state for any finite values of coupling strength $t/J$ (with t as hopping and J as exchange); in 2D and 3D cubic lattices the spin gaps are found to vanish continuously around (t/J)c≈0.70 and (t/J)c≈0.38, respectively, where quantum phase transitions occur and the Kondo spin liquid state changes into an antiferromagnetically long-range ordered state. These results are in agreement with variational Monte Carlo, higher-order series expansion, and recent quantum Monte Carlo calculations for the symmetric Kondo lattice model.