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arXiv:0912.3881 · Physical Review Letters

Magnetic Impurities in the Honeycomb Kitaev Model

Kusum Dhochak, Ravi Shankar, Vikram Tripathi

Published Sep 7, 2010• 50 citations
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Abstract

We study the effect of coupling magnetic impurities to the honeycomb lattice spin-$1/2$ Kitaev model in its spin-liquid phase. We show that a spin-$S$ impurity coupled to the Kitaev model is associated with an unusual Kondo effect with an intermediate coupling unstable fixed point ${K}_{c}\ensuremath{\sim}J/S$ separating topologically distinct sectors of the Kitaev model. We also show that the massless spinons in the spin-liquid mediate an interaction of the form ${S}_{i\ensuremath{\alpha}}^{2}{S}_{j\ensuremath{\beta}}^{2}/{R}_{ij}^{3}$ between distant impurities unlike the usual dipolar RKKY interaction ${S}_{i\ensuremath{\alpha}}{S}_{j\ensuremath{\alpha}}/{R}_{ij}^{3}$ noted in various 2D impurity problems with a pseudogapped density of states of the spin bath. Furthermore, this long-range interaction is possible only if the impurities (a) couple to more than one neighboring spin on the host lattice and (b) the impurity spin $S\ensuremath{\ne}1/2$.

DOI
10.1103/physrevlett.105.117201

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We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2{Z}_{2}Z2​ frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow flow toward a stable strong-coupling state. Since the low-energy bosons exist around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.