Local Kondo entanglement and symmetry protected local criticality in the two-impurity Kondo problem

Abstract

The local Kondo entanglement is defined as the concurrence of a short-ranged Kondo singlet state consisting of a localized magnetic moment and a nearby conduction electron. We derive the entanglement phase diagram of the Rasul-Schlottmann model, the effective spin-only Hamiltonian for the two-impurity Kondo model in the numerical renormalization group approach. We show that the local Kondo entanglement vanishes exactly at the two-impurity Kondo critical point, associated concomitantly with a jump in the inter-impurity entanglement. We discuss how to generalize this result to a Kondo lattice model preserving the same enhanced spin symmetry.