Anomalous Curie response of an impurity in a quantum critical spin-$1/2$ Heisenberg antiferromagnet*

There is a disagreement concerning the low-temperature ($T$) magnetic susceptibility $\chi ^z_{{\rm imp}}\sim {\mathcal C}/T$ of a spin-$S$ impurity in a nearly quantum critical antiferromagnetic host. Field-theoretical work~[1] predicted an anomalous Curie constant $S^2/3<{\mathcal C}0$ quantum Monte Carlo simulations in order to resolve the controversy. Our main result is for a vacancy in a quantum critical spin-$1/2$ Heisenberg antiferromagnet on a bilayer lattice. In our susceptibility data for the $S=1/2$ impurity we observe a Curie constant ${\mathcal C}=0.262(2)$. Although the value falls outside the predicted range, it should correspond to an anomalous impurity response, as proposed in Ref.~[1]. [1]~S.~Sachdev, C.~Buragohain, and M.~Vojta, Science \textbf{286}, 2479 (1999); M.~Vojta, C.~Buragohain, and S.~Sachdev, Phys. Rev. B \textbf{61}, 15152 (2000). [2]~O.~P.~Sushkov, Phys. Rev. B \textbf{62}, 12135 (2000). [3]~M.~Troyer, Prog. Theor. Phys. Supp. \textbf{145}, 326 (2002).