  We study exactly the effect of an impurity in the interacting quantum spin
chain at low temperature by solving the integrable spin-1/2 XXZ periodic chain
with an impurity through the algebraic and thermal Bethe ansatz methods. In
particular, we investigate how the crossover temperature for the impurity
specific heat depends on the impurity parameter, i.e. the coupling of the
impurity to other spins, and show that it is consistent with the analytic
expression that is obtained by setting the impurity susceptibility to be
proportional to the inverse of the crossover temperature. In the model, two
types of crossover behavior appear: one from the high-temperature regime to the
low-temperature Kondo regime and another from the N-site homogeneous chain to
the (N-1)-site chain with a decoupled free impurity spin, with respect to the
temperature and the impurity parameter, respectively.
