Quantum critical point in a periodic Anderson model

Abstract

We investigate the symmetric periodic Anderson model (PAM) on a three-dimensional cubic lattice with nearest-neighbor hopping and hybridization matrix elements. Using Gutzwiller's variational method and the Hubbard-III approximation (which corresponds to an exact solution of the appropriate Falicov-Kimball model in infinite dimensions) we demonstrate the existence of a quantum critical point at zero temperature. Below a critical value Vc of the hybridization (or above a critical interaction Uc) the system is an insulator in Gutzwiller's and a semimetal in Hubbard's approach, whereas above Vc (below Uc) it behaves like a metal in both approximations. These predictions are compared with the density of states of the d and f bands calculated from quantum Monte Carlo and numerical renormalization group calculations. Our conclusion is that the half-filled symmetric PAM contains a metal-semimetal transition, not a metal-insulator transition as has been suggested previously.