  We formulate a general cluster Dual Fermion Approach to nonlocal correlations
in crystals. The scheme allows the treatment of long-range correlations beyond
cluster DMFT and nonlocal effects in realistic calculations of multiorbital
systems. We show that the the simplest approximation exactly corresponds to
free cluster DMFT. We further consider the relation between the two-particle
Green functions in real and dual variables. We apply this approach by
calculating the Green function of the Hubbard model in one dimension starting
from the two-site cluster DMFT solution. The result agrees well with the Green
function obtained from a DMRG calculation.
