Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

We recently introduced the dynamical cluster approximation ~DCA!, a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation ~exact result! is obtained by taking the cluster to a single site ~the thermodynamic limit!. Here, we provide details of our method, explicitly show that it is causal, systematic, F derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.