Quantum impurity in an antiferromagnet: non-linear sigma model theory

TL;DR

This paper develops a non-linear sigma model approach to describe quantum impurities in antiferromagnets, deriving low-temperature susceptibilities and analyzing impurity behavior near quantum critical points.

Contribution

It introduces a new formulation using the O(3) non-linear sigma model for quantum impurities in antiferromagnets, including critical behavior analysis.

Findings

Derived low-temperature impurity spin susceptibilities.

Analyzed impurity effects near quantum criticality.

Identified the Berry phase as an exactly marginal perturbation.

Abstract

We present a new formulation of the theory of an arbitrary quantum impurity in an antiferromagnet, using the O(3) non-linear 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 to the gapped paramagnet (d is the spatial dimension): the impurity is described solely by a topological Berry phase term which is an exactly marginal perturbation to the critical theory. The physical properties of the quantum impurity near criticality are obtained by an expansion in (d-1).