We investigate the symmetric periodic Anderson model ͑PAM͒ 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 dimensions͒ we demonstrate the existence of a quantum critical point at zero temperature. Below a critical value V c of the hybridization ͑or above a critical interaction U c ) the system is an insulator in Gutzwiller's and a semimetal in Hubbard's approach, whereas above V c ͑below U c ) 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
