Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

We recently introduced the dynamical cluster approximation (DCA), a techniq ue that includes short-ranged dynamical correlations in addition to the loc al dynamics of the dynamical mean-field approximation while preserving caus ality. 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 thermodyna mic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, Phi derivable, and that it becomes conserving as th e cluster size increases. We demonstrate the DCA by applying it to a quantu m Monte Carlo and exact enumeration study of the two-dimensional Falicov-Ki mball model. The resulting spectral functions preserve causality, and the s pectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases .