SPIN LADDERS WITH NONMAGNETIC IMPURITIES

We investigate antiferromagnetic spin ladders with nonmagnetic impurit ies by variational and numerical [Lanczos and density matrix renormali zation group (DMRG)] methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchang e interaction J(eff), the magnitude of which depends on the impurity d istance. The magnitude of J(eff) is different for unpaired spins at th e edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of t he ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy l evels for up to six impurities and find that these spectra can be repr oduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and arg ue that in the thermodynamic limit the spin ladder with a finite conce ntration of impurities always shows a Curie susceptibility at low temp eratures.