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Motivated by both experimental and theoretical activities, we discuss thefate of Kondo screening and possible quantum phase transitions inantiferromagnetically ordered phases of Kondo lattices. While transitions withtopological changes of the Fermi surface may occur, we demonstrate that anentirely continuous evolution from itinerant to local-moment antiferromagnetism(i.e. from strong to negligible Kondo screening) is possible as well. Thissituation is in contrast to that in a non-symmetry-broken situation where aquantum phase transition towards an exotic metallic spin-liquid statenecessarily accompanies the disappearance of Kondo screening. We discusscriteria for the existence of topological transitions in the antiferromagneticphase, as well as implications for theoretical scenarios and for currentexperiments.

From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity vs. quantum phase transitions