We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent γ=2 for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with γ=1 instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibility below and above the quantum critical point, respectively.
Magnetic susceptibility of a periodic Anderson model defined in infinite dimensions is investigated using the quantum Monte Carlo method. Special attention is paid to the enhancement of the interband contribution to the susceptibility (the Van Vleck term). It is found that the interband contribution is enhanced by the electron-electron interaction, but the enhancement is weaker than the dynamical mass enhancement. In particular, when the mixing between conduction electrons and f -electrons is small compared to the bandwidth, the enhancement of the interband contribution becomes much smaller than the dynamical mass enhancement as the interaction becomes strong.
We study quantum criticality in the doped two-dimensional periodic Anderson model with the hybridization acting as a tuning parameter. Employing the dynamical vertex approximation we find two distinct quantum critical behaviors. One is a quantum critical point between the antiferromagnetically ordered and the Kondo state, both metallic with itinerant
f electrons. Here, we obtained the critical exponent
γ≈1 for the temperature dependence of the antiferromagnetic susceptibility. We observe a \emph{second} quantum critical behavior with
γ=2 above the continuing zero-temperature magnetic order, at a quantum critical point where the
f electrons turn from localized to itinerant.