Universal Dephasing Rate due to Diluted Kondo Impurities

We calculate the dephasing rate due to magnetic impurities in a weakly disordered metal as measured in a weak-localization experiment. If the density ${n}_{\mathrm{S}}$ of magnetic impurities is sufficiently low, the dephasing rate $1/{\ensuremath{\tau}}_{\ensuremath{\varphi}}$ is a universal function, $1/{\ensuremath{\tau}}_{\ensuremath{\varphi}}=({n}_{\mathrm{S}}/\ensuremath{\nu})f(T/{T}_{\mathrm{K}})$, where ${T}_{\mathrm{K}}$ is the Kondo temperature and $\ensuremath{\nu}$ is the density of states. We show that inelastic vertex corrections with a typical energy transfer $\ensuremath{\Delta}E$ are suppressed by powers of $1/({\ensuremath{\tau}}_{\ensuremath{\varphi}}\ensuremath{\Delta}E)\ensuremath{\propto}{n}_{\mathrm{S}}$. Therefore, the dephasing rate can be calculated from the inelastic cross section proportional to $\ensuremath{\pi}\ensuremath{\nu}\text{ }\mathrm{Im}T\ensuremath{-}|\ensuremath{\pi}\ensuremath{\nu}T{|}^{2}$, where $T$ is the $T$ matrix which is evaluated numerically exactly using the numerical renormalization group.