Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
  We introduce an extension of the dynamical mean field approximation (DMFA) which retains the causal properties and generality of the DMFA, but allows for systematic inclusion of non-local corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to one (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 non-local correlations suppress the CDW transition temperature. \ 
M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H.   R. Krishnamurthy