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We generalized the recently introduced new impurity solver based on thediagrammatic expansion around the atomic limit and Quantum Monte Carlosummation of the diagrams. We present generalization to the cluster ofimpurities, which is at the heart of the cluster Dynamical Mean-Field methods,and to realistic multiplet structure of a correlated atom, which will allow ahigh precision study of actinide and lanthanide based compounds with thecombination of the Dynamical Mean-Field theory and band structure methods. Theapproach is applied to both, the two dimensional Hubbard and t-J model withinCellular Dynamical Mean Field method. The efficient implementation of the newalgorithm, which we describe in detail, allows us to study coherence of thesystem at low temperature from the underdoped to overdoped regime. We show thatthe point of maximal superconducting transition temperature coincides with thepoint of maximum scattering rate although this optimal doped point appears atdifferent electron densities in the two models. The power of the method isfurther demonstrated on the example of the Kondo volume collapse transition inCerium. The valence histogram of the DMFT solution is presented showing theimportance of the multiplet splitting of the atomic states.Comment: 12 pages, 4 figure

Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base