Quantum Magnetic Impurities in Magnetically Ordered Systems

We discuss the problem of a spin $1/2$ impurity immersed in a spin $S$ magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group methods and accurate numerical renormalization group we show that contrary to other dissipative models there is quantum frustration of decoherence and quasiscaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility. Our results may also have relevance to quantum computation.

Figure 1

RG flow in the ${\kappa }_1\times {\kappa }_2$ plane.

Figure 2

${\chi }_{\perp }^{\prime \prime }(\omega ,\alpha )/\omega$ as a function of $\omega /T_A$.

Figure 3

${\chi }_{\perp }^{\prime \prime }(\omega )/\omega$ as a function of $\omega /D$.