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We investigate the symmetric Periodic Anderson Model (PAM) on athree-dimensional cubic lattice with nearest-neighbor hopping and hybridizationmatrix elements. Using Gutzwiller's variational method and the Hubbard-IIIapproximation (which corresponds to the exact solution of an appropriateFalicov-Kimball model in infinite dimensions) we demonstrate the existence of aquantum critical point at zero temperature. Below a critical value $V_c$ of thehybridization (or above a critical interaction $U_c$) the system is an {\eminsulator} in Gutzwiller's and a {\em semi-metal} in Hubbard's approach,whereas above $V_c$ (below $U_c$) it behaves like a metal in bothapproximations. These predictions are compared with the density of states ofthe $d$- and $f$-bands calculated from Quantum Monte Carlo and NRGcalculations. Our conclusion is that the half-filled symmetric PAM contains a{\em metal-semimetal transition}, not a metal-insulator transition as has beensuggested previously.

Quantum critical point in a periodic Anderson model