  We generalized the recently introduced new impurity solver based on the
diagrammatic expansion around the atomic limit and Quantum Monte Carlo
summation of the diagrams. We present generalization to the cluster of
impurities, which is at the heart of the cluster Dynamical Mean-Field methods,
and to realistic multiplet structure of a correlated atom, which will allow a
high precision study of actinide and lanthanide based compounds with the
combination of the Dynamical Mean-Field theory and band structure methods. The
approach is applied to both, the two dimensional Hubbard and t-J model within
Cellular Dynamical Mean Field method. The efficient implementation of the new
algorithm, which we describe in detail, allows us to study coherence of the
system at low temperature from the underdoped to overdoped regime. We show that
the point of maximal superconducting transition temperature coincides with the
point of maximum scattering rate although this optimal doped point appears at
different electron densities in the two models. The power of the method is
further demonstrated on the example of the Kondo volume collapse transition in
Cerium. The valence histogram of the DMFT solution is presented showing the
importance of the multiplet splitting of the atomic states.
