Renormalization in the One-Dimensional Kondo Lattice: the Nozières Criterion

We apply second-order renormalization to the functional integral representation of the one-dimensional Kondo lattice, as expressed in terms of Grassmann variables for both spins and carriers. We find that the Nozières criterion is verified throughout the weak-coupling limit of validity of the method. The Kondo instability can only prevail when the coherence length at the Kondo temperature is smaller than the inter-spin distance. There is otherwise incomplete Kondo screening and the lattice eventually becomes unstable with respect to the formation of an RKKY spin-density wave.