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The Falicov-Kimball model with a correlated-hopping interaction is solvedusing an extended dynamical mean-field theory that becomes exact in the limitof large dimensions. The effect of correlated hopping is to introduce nonlocalself-energy components that retain full dynamics as D goes to infinity, thusintroducing an explicit k-dependence to the single-particle self-energy. Anexplicit solution for the homogeneous phase at D = 2 reveals significantnonlocal dynamical contributions in the physically relevant regime of amoderately large correlated-hopping amplitude, indicating that importantnonlocal correlations are omitted in Hubbard-like models upon neglecting thecorrelated-hopping interaction.Comment: 4 pages, 4 figures; to appear in Phys. Rev.

Correlated hopping in the Falicov-Kimball model: A large-dimensions study