Theory of quantum impurities in spin liquids

TL;DR

This paper investigates the behavior of impurities in certain gapless spin liquids using conformal field theory, revealing universal impurity responses and correcting previous theories, with implications for high-temperature superconductors.

Contribution

It introduces a gauge theory framework for impurities in U(1) spin liquids, showing universal impurity susceptibility and correcting earlier vacancy models.

Findings

Impurity susceptibility follows a 1/T law with a universal Curie constant.

Magnetic field does not induce staggered magnetization in the sF state.

The gauge theory provides a more accurate description than previous models.

Abstract

We describe spin correlations in the vicinity of a generalized impurity in a wide class of fractionalized spin liquid states. We argue that the primary characterization of the impurity is its electric charge under the gauge field describing singlet excitations in the spin liquid. We focus on two gapless U(1) spin liquids described by 2+1 dimensional conformal field theories (CFT): the staggered flux (sF) spin liquid, and the deconfined critical point between the Neel and valence-bond-solid (VBS) states. In these cases, the electric charge is argued to be an exactly marginal perturbation of the CFT. Consequently, the impurity susceptibility has a 1/T temperature dependence, with an anomalous Curie constant which is a universal number associated with the CFT. One unexpected feature of the CFT of the sF state is that an applied magnetic field does not induce any staggered spin polarization in the vicinity of the impurity (while such a staggered magnetization is present for the Neel-VBS case). These results differ significantly from earlier theories of vacancies in the sF state, and we explicitly demonstrate how our gauge theory corrects these works. We discuss implications of our results for the cuprate superconductors and organic Mott insulators.