Magnetic impurities coupled to quantum antiferromagnets in one dimension

Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.