Analysis of the dynamical cluster approximation for the Hubbard model

We examine a central approximation of the recently introduced dynamical cluster approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study noncompact and compact contributions to the thermodynamic potential. We show that approximating noncompact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas noncompact graphs should be inferred from the appropriate Dyson equation. The distinction between noncompact and compact diagrams persists even in the limit of infinite dimensions. Nonlocal corrections beyond the DCA exist for the noncompact diagrams, whereas they vanish for compact diagrams.