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Quantum criticality in certain heavy-fermion metals is believed to go beyondthe Landau framework of order-parameter fluctuations. In particular, there isconsiderable evidence for Kondo destruction: a disappearance of the staticKondo singlet amplitude that results in a sudden reconstruction of Fermisurface across the quantum critical point and an extra critical energy scale.This effect can be analyzed in terms of a dynamical interplay between the Kondoand RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondoresonance is lost, but Kondo singlet correlations remain at nonzerofrequencies. This dynamical effect allows for mass enhancement in theKondo-destroyed phase. Here, we elucidate the dynamical Kondo effect inBose-Fermi Kondo/Anderson models, which unambiguously exhibit Kondo-destructionquantum critical points. We show that a simple physical quantity---theexpectation value $\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle$ for the dotproduct of the local ($f$) and conduction-electron ($c$) spins---variescontinuously across such quantum critical points. A nonzero $\langle {\bfS}_{f} \cdot {\bf s}_{c} \rangle$ manifests the dynamical Kondo effect thatoperates in the Kondo-destroyed phase. Implications are discussed for thestability of Kondo-destruction quantum criticality as well as the understandingof experimental results in quantum critical heavy-fermion metals.

Dynamical Kondo effect and Kondo destruction in effective models for quantum-critical heavy fermion metals