EQUIVALENCE OF VARIATIONAL AND SLAVE-BOSON MEAN-FIELD TREATMENTS OF THE PERIODIC ANDERSON MODEL

We investigate Gutzwiller-correlated wave functions as variational ground states for the periodic Anderson model. We extend a recently developed technique for the Hubbard model to the case of two hybridized bands with degeneracy N. We calculate expectation values in the following limits: dilute system (single-impurity case), large degeneracy N, and large dimension d. The mean-field results using the slave-boson approach of Coleman and of Kotliar and Ruckenstein are reproduced in the large-N and large-d limit, respectively. These techniques, therefore, obey variational principles at T = 0 in the respective limits and their applicability for T > 0 is naturally limited to the Fermi-liquid regime. Evaluations of Gutzwiller-correlated wave functions using the "Gutzwiller approximation" are seen to become exact in the limit of large dimensions. A systematic expansion in 1/d can be performed for N = 2. In general, corrections are small, of order 1/(dN).