Bosonization solution of the Kondo lattice in a Luttinger liquid

We address the physics of a regular arrangement of independent magnetic impurities embedded in a band of interacting electrons. We focus on the one-dimensional case that can be studied using bosonization and in which the electron bulk is described by a Luttinger liquid. The impurity spins interact with the electrons via magnetic exchange that introduces the possibility of Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) physics. We find that for two special values of the interactions, the model can be refermionized as a noninteracting electron band hybridized with a regular array of resonant levels. These solvable limits provide access to impurity correlators that correspond to either extended algebraic order or local screening. A physical picture emerges of how the interelectron interactions can stabilize either Kondo or RKKY physics depending on the sign of the interaction.