  The Falicov-Kimball model with a correlated-hopping interaction is solved
using an extended dynamical mean-field theory that becomes exact in the limit
of large dimensions. The effect of correlated hopping is to introduce nonlocal
self-energy components that retain full dynamics as D goes to infinity, thus
introducing an explicit k-dependence to the single-particle self-energy. An
explicit solution for the homogeneous phase at D = 2 reveals significant
nonlocal dynamical contributions in the physically relevant regime of a
moderately large correlated-hopping amplitude, indicating that important
nonlocal correlations are omitted in Hubbard-like models upon neglecting the
correlated-hopping interaction.
