Nonlocal dynamical correlations of strongly interacting electron systems

We introduce an extension of the dynamical mean-field approximation ~DMFA! that retains the causal properties and generality of the DMFA, but allows for systematic inclusion of nonlocal corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA ~exact result! is recovered as the cluster size goes to 1 ~infinity!. As a demonstration, we study the Falicov-Kimball model using a variety of cluster sizes. We show that the sum rules are preserved, the spectra are positive definite, and the nonlocal correlations suppress the charge-density wave transition temperature. @S0163-1829~98!51436-1#