Kondo effect in a Luttinger liquid

We treat the Kondo effect in one-dimensional interacting systems. We find that for repulsive interaction and off half filling, the Kondo temperature ${\mathit{T}}_{\mathit{K}}$∝(J${\mathrm{\tau }}_0$ ${)}^{2/\mathrm{\eta }}$, where η is the nonuniversal spin-density-wave exponent of the host system, J the Kondo coupling, and ${\mathrm{\tau }}_0$ the short-time cutoff. We also show that the wave-function orthogonality theorem remains true in a Luttinger liquid except that interactions reduce the power with which the overlap vanishes in the thermodynamic limit.