ELECTRON CORRELATION IN THE PERIODIC ANDERSON MODEL IN D = +INFINITY DIMENSIONS

The periodic Anderson model with strong repulsion is studied. The leading-order effects with respect to 1/d, d being the dimensionality of the system, are Kondo-effect-type local spin fluctuations and mean-field-approximation-type magnetic orders. The competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida exchange interaction determines whether the ground state is magnetic or paramagnetic. A single-site approximation (SSA) is rigorous for paramagnetic states in d --> + infinity dimensions. The SSA reduces the problem to solving the Anderson model. A "local" Kondo temperature is defined to show an energy scale of the local spin fluctuations. On the other hand, an SSA including magnetic mean fields is rigorous for magnetic states in d --> + infinity dimensions. All the other effects are of higher order: Critical and intersite spin fluctuations are O(1/square-root d); and paramagnetic orders are at most O(1/d). The 1/d expansion is one of the most useful methods for examining lower-temperature phases in real dimensions.