  The Kondo effect in a one-dimensional spin-1/2 XXZ model in the gapless XY
regime (-1<Delta<=1) is studied both analytically and numerically. In our model
an impurity spin (S=1/2) is coupled to a single spin in the XXZ spin chain.
Perturbative renormalization-group (RG) analysis is performed for various
limiting cases to deduce low-energy fixed points. It is shown that in the
ground state the impurity spin is screened by forming a singlet with a spin in
the host XXZ chain. In the antiferromagnetic side (0<Delta<=1) the host chain
is cut into two semi-infinite chains by the singlet. In the ferromagnetic side
(-1<Delta<0), on the other hand, the host XXZ chain remains as a single chain
through "healing" of a weakened bond in the low-energy (long-distance) limit.
The density matrix renormalization group method is used to study the size
scaling of finite-size energy gaps and the power-law decay of correlation
functions in the ground state. The numerical results are in good agreement with
the predictions of the RG analysis. Low-temperature behaviors of specific heat
and susceptibility are also discussed.
