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We analyze cellular dynamical mean-field theory (CDMFT) and the dynamicalcluster approximation (DCA). We derive exact sum-rules for the hybridizationfunctions and give examples for DMFT, CDMFT, and DCA. For impurity solversbased on a Hamiltonian, these sum-rules can be used to monitor convergence ofthe bath-parametrization. We further discuss how the symmetry of the clusternaturally leads to a decomposition of the bath Green matrix into irreduciblecomponents, which can be parametrized independently, and give an explicitrecipe for finding the optimal bath-parametrization. As a benchmark we revisitthe one-dimensional Hubbard model. We carefully analyze the evolution of thedensity as a function of chemical potential and find that, close to the Motttransition, convergence with cluster size is unexpectedly slow. In twodimensions we find, that we need so many bath-sites to obtain a reliableparametrization that Lanczos calculations are hardly feasible with currentcomputers. For such large baths our symmetry-adapted approach should provecrucial for finding a reliable bath-parametrization.

Sum-rules and bath-parametrization for quantum cluster theories