Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors

We present the universal theory of arbitrary, localized impurities in a con fining paramagnetic state of two-dimensional antiferromagnets with global S U(2) spin symmetry. The energy gap of the host antiferromagnet to spin-1 ex citations, Delta, is assumed to be significantly smaller than a typical nea rest neighbor exchange. In the absence of impurities, it was argued in earl ier work [Chubukov et al., Phys. Rev. B 49, 11 919 (1994)] that the low-tem perature quantum dynamics is universally and completely determined by the v alues of Delta and a spin-wave velocity c. Here we establish the remarkable fact that no additional parameters are necessary for an antiferromagnet wi th a dilute concentration of impurities, n(imp)-each impurity is completely characterized by a integer/half-odd-integer valued spin S which measures t he 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)(hc)(2)/ Delta, and we predict a universal, asymmetric line shape for the collective mode peak We argue that, under suitable conditions, our results apply unch anged (or in some cases, with minor modifications) to d-wave superconductor s, and compare them to recent neutron-scattering experiments on YBa2Cu3O7 b y pong et al. [Phys. Rev. Lett. 82, 1939 (1999)]. We also describe the univ ersal evolution of numerous measurable correlations as the host antiferroma gnet undergoes a quantum phase transition to a Neel ordered state.