  Competition between the Kondo effect and Ruderman-Kittel-Kasuya-Yosida
interaction in the two-impurity Kondo problem can be phenomenologically
described by the Rasul-Schlottmann spin model. We revisit this model from the
quantum entanglement perspective by calculating both the inter-impurity
entanglement and the local Kondo entanglement, the latter being the
entanglement between a local magnetic impurity and its spatially nearby
conduction electron. A groundstate phase diagram is derived and a discontinuous
breakdown of the local Kondo entanglement is found at the singular point,
associated concomitantly with a jump in the inter-impurity entanglement. An
entanglement monogamy holds in the whole phase diagram. Our results identify
the important role of the frustrated cross-coupling and demonstrate the local
characteristic of the quantum phase transition in the two-impurity Kondo
problem. The implications of these results for Kondo lattices and quantum
information processing are also briefly discussed.
