Quantum impurity in an antiferromagnet: Nonlinear sigma model theory

We present a formulation of the theory of an arbitrary quantum impurity in an antiferromagnet, using the $O\left(3\right)\mathrm{}$ nonlinear sigma model. We obtain the low-temperature expansion for the impurity spin susceptibilities of antiferromagnets with magnetic long-range order in the ground state. We also consider the bulk quantum phase transition in $d=2\mathrm{}$ to the gapped paramagnet $(d$ is the spatial dimension): The impurity is described solely by a topological Berry phase term that is an exactly marginal perturbation to the critical theory. The physical properties of the quantum impurity near criticality are obtained by an expansion in $\left(d-1\right).$