Entanglement entropy near Kondo-destruction quantum critical points

Entanglement entropy is a measure of quantum-mechanical entanglement across the boundary created by partitioning a system into two subsystems. We study this quantity in Kondo impurity models that feature Kondo-destruction quantum critical points (QCPs). Recent work [1] has shown that the entanglement entropy between a Kondo impurity of spin $S_\mathrm{imp}$ and its environment is pinned at its maximum possible value $S_e=\ln(2S_{\mathrm{imp}}+1)$ throughout the Kondo phase. In the Kondo-destroyed phase, where the impurity spin acquires a nonzero expectation value $M_\mathrm{loc}$, $S_e = \ln(2 S_{\mathrm{imp}}+1)- a(S_{\mathrm{imp}}) M^2_\mathrm{loc}$ irrespective of the properties of the host. Here, we report numerical renormalization-group results for Kondo models with a pseudogapped density of states under a different partition that separates the impurity and on-site conduction electrons from the rest of the system. Now, the entanglement entropy is affected by the nature of the environment beyond the information contained in $M_{\mathrm{loc}}$, but $S_e$ still contains a critical part that exhibits power-law behavior in the vicinity of the Kondo-destruction QCP. [1] J. H. Pixley \emph{et. al.}, Phys. Rev. B \textbf{91}, 245122 (2015).