Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors

We present the universal theory of arbitrary, localized impurities in a confining paramagnetic state of two-dimensional antiferromagnets with global SU(2) spin symmetry. The energy gap of the host antiferromagnet to spin-1 excitations, \Delta, is assumed to be significantly smaller than a typical nearest neighbor exchange. In the absence of impurities, it was argued in earlier work (Chubukov et al. cond-mat/9304046) that the low-temperature quantum dynamics is universally and completely determined by the values of \Delta and a spin-wave velocity c. Here we establish the remarkable fact that no additional parameters are necessary for an antiferromagnet with a dilute concentration of impurities, n_{imp} - each impurity is completely characterized by a integer/half-odd-integer valued spin, S, which measures the net uncompensated Berry phase due to spin precession in its vicinity. We compute the impurity-induced damping of the spin-1 collective mode of the antiferromagnet: the damping occurs on an energy scale \Gamma= n_{imp} (\hbar c)^2/\Delta, and we predict a universal, asymmetric lineshape for the collective mode peak. We argue that, under suitable conditions, our results apply unchanged (or in some cases, with minor modifications) to d-wave superconductors, and compare them to recent neutron scattering experiments on YBCO by Fong et al. (cond-mat/9812047). We also describe the universal evolution of numerous measurable correlations as the host antiferromagnet undergoes a quantum phase transition to a Neel ordered state.