The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-
1/2 XY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's
g factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.
We study by Monte Carlo simulations a magnetic impurity coupled antiferromagnetically to a one-dimensional quantum spin model. The impurity susceptibility and the spin-correlation function are calculated. By defining and evaluating an energy scale from the inverse of the impurity susceptibility at zero temperature, we find a scaling relation for the impurity susceptibility in agreement with the prediction of the conformal field theory. We analyze the problem by mapping the spin model onto the resonant-level model, and interpret the energy scale as the resonant-level width. The spin-correlation function between the impurity spin and the spins in the chain is found to extend over long range at low temperatures. We show that the system can be considered as a model of an insulator with heavy-fermion behavior.