Long-range entanglement near a Kondo-destruction quantum critical point

Abstract

The numerical renormalization group is used to study quantum entanglement in the Kondo impurity model with a pseudogapped density of states $\rho (\epsilon )\propto |\epsilon {|}^r$ ($r>0$) that vanishes at the Fermi energy $\epsilon =0$. The model features a Kondo-destruction quantum critical point (QCP) separating a partially screened phase (reached for impurity-band exchange couplings $J>J_c$) from a local-moment phase ($J<J_c$). The impurity contribution $S_e^{imp}$ to the entanglement entropy between a region of radius $R$ around the magnetic impurity and the rest of the host system reveals a characteristic length scale $R^{\ast }$ that distinguishes a regime $R\ll R^{\ast }$ of maximal critical entanglement from one $R\gg R^{\ast }$ of weaker entanglement. Within each phase, $S_e^{imp}$ is a universal function of $R/R^{\ast }$ with a power-law decay for $R/R^{\ast }\gg 1$. The entanglement length scale $R^{\ast }$ diverges on approach to the QCP with a critical exponent that depends only on $r$.

16 pages, 12 figures, includes supplemental information