The dynamical cluster approximation: A new technique for simulations of strongly correlated electron systems

We present the algorithmic details of the dynamical cluster approximation (DCA) algorithm. The DCA is a fully-causal approach which systematically restores nonlocal correlations to the dynamical mean field approximation (DMFA). The DCA is in the thermodynamic limit and becomes exact for an infinite cluster size, while reducing to the DMFA for a cluster size of unity. Using the one-dimensional Hubbard Model as a nontrivial test of the method, we systematically compare the results of a quantum Monte Carlo (QMC) based DCA with those obtained by finite-size QMC simulations (FSS). We find that the single-particle Green function and the self-energy of the DCA and FSS approach the same limit as the system size is increased, but horn complimentary directions. The utility of the DCA in addressing problems that have not been resolved by FSS is demonstrated.