An effective Lagrangian for the continuous transition in an extended Kondo lattice model

We propose an effective Lagrangian for the continuous transition from the heavy fermion metal to the antiferromagnetic metal in an extended Kondo lattice model. Based on the slave-boson representation we introduce an additional new order parameter associated with difference of the chemical potential between conduction electrons $c_{i\sigma}$ and local spinons $f_{i\sigma}$. This order parameter allows pseudospin construction $T_{ix} = {1/2}<{c}_{i\alpha}^{\dagger}f_{i\alpha} + f_{i\alpha}^{\dagger}c_{i\alpha}>$, $T_{iy} = - \frac{i}{2}<{c}_{i\alpha}^{\dagger}f_{i\alpha} - f_{i\alpha}^{\dagger}c_{i\alpha}>$, and $T_{iz} = {1/2}<{c}_{i\alpha}^{\dagger}c_{i\alpha} - f_{i\alpha}^{\dagger}f_{i\alpha}>$, where $T_{i\pm} = T_{ix} \pm iT_{iy}$ corresponds to the usual hybridization order parameter in the slave-boson representation of the Kondo lattice model. The resulting effective action is shown to be an anisotropic pseudospin model with a Landau damping term for the screened-unscreened (XY$-$Ising) phase transition. To describe the emergence of antiferromagnetic order in the unscreened (Ising) phase, we phenomenologically introduce the antiferromagnetic Heisenberg model for the localized spins, where the effective coupling strength is given by $J_{eff} = J|<{T}_{iz}>|^{2}$. This ad-hoc construction allows the continuous transition from the heavy fermion phase to the antiferromagnetic phase because breakdown of Kondo screening ($<{T}_{i\pm}> = 0$ and $<{T}_{iz}> \not= 0$) causes effective exchange interactions between unscreened local moments.