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Local Kondo entanglement and its breakdown in an effective two-impurity Kondo model

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.