Phase diagram of an impurity in the spin-1/2 chain: Two-channel Kondo effect versus Curie law

We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J(1) and the coupling between the two sites J(2). By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a nontrivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi-liquid fixed point with a logarithmically diverging impurity susceptibility as in the two-channel Kondo effect. Our results resolve a controversy about the renormalization flow.