Universal Crossover Behavior of a Magnetic Impurity and Consequences for Doping in Spin-1/2Chains

We consider a magnetic impurity in the antiferromagnetic spin- $1/2$ chain which is equivalent to the two-channel Kondo problem in terms of the field theoretical description. Using a modification of the transfer-matrix density matrix renormalization group we are able to determine the crossover function for the impurity susceptibility over a large temperature range, which exhibits universal data collapse. We also calculate the local susceptibilities near the impurity, which show an interesting competition of boundary effects. This results in quantitative predictions for experiments on doped spin- $1/2$ chains, which could observe two-channel Kondo physics directly.