Coherence Scale of the Kondo Lattice

It is shown that the large- $N$ approach yields two energy scales for the Kondo lattice model. The single-impurity Kondo temperature, $T_K$, signals the onset of local singlet formation, while Fermi-liquid coherence sets in only below a lower scale, $T^{\star }$. At low conduction electron density $n_c$ (“exhaustion” limit), the ratio $T^{\star }/T_K$ is much smaller than unity, and is shown to depend only on $n_c$ and not on the Kondo coupling. The physical meaning of these two scales is demonstrated by computing several quantities as a function of $n_c$ and temperature.