Spatial structure of entanglement in a system near a Kondo destruction quantum critical point

We use entanglement entropy as a probe of the ground state of the pseudogap Kondo model near a quantum critical point (QCP) that separates a Kondo-screened phase (reached for impurity-band exchange couplings $J>J_c$) from a Kondo-destroyed or local-moment phase ($J < J_c$). The impurity contribution to the entanglement entropy between a region of radius $R$ around the magnetic impurity and the rest of the semimetallic host reveals a characteristic length scale $R^*$ that distinguishes a regime $R\ll R^*$ of maximal critical entanglement from one $R\gg R^*$ of weaker entanglement. In contrast to the conventional case of a metallic host, entanglement in the Kondo phase remains nonzero for $R\gg R^*$, suggesting that the Kondo screening cloud is infinite. In the local-moment phase, the strong entanglement for $R\ll R^*$ evidences a dynamical Kondo effect, but the entanglement decreases toward zero for $R \gg R^*$. Within each phase, the impurity entanglement entropy computed via the numerical renormalization group is well described as a universal function of $R/R^*$. The value of $R^*$ diverges on approach to the QCP like $|J-J_c|^{-\nu}$, where $\nu$ is the correlation length exponent, leading to maximal entanglement extending throughout the entire system.