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The dynamical cluster approximation (DCA) is a quantum cluster extension to the single-site dynamical mean-field theory that incorporates spatially nonlocal dynamic correlations systematically and nonperturbatively. The DCA$^+$ algorithm addresses the cluster shape dependence of the DCA and improves the convergence with cluster size by introducing a lattice self-energy with continuous momentum dependence. However, we show that the DCA$^+$ algorithm is plagued by a fundamental problem when its self-consistency equations are formulated using the bare Greens function of the cluster. This problem is most severe in the strongly correlated regime at low doping, where the DCA$^+$ self-energy becomes overly metallic and local, and persists to cluster sizes where the standard DCA has long converged. In view of the failure of the DCA$^+$ algorithm, we propose to complement DCA simulations with a post-interpolation procedure for single-particle and two-particle correlation functions to preserve continuous momentum dependence and the associated benefits in the DCA. We demonstrate the effectiveness of this practical approach with results for the half-filled and hole-doped two-dimensional Hubbard model.
I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a cluster so
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 non-compact and compact contributions to the thermodynamic potential.
We examine the cluster-size dependence of the cellular dynamical mean-field theory (CDMFT) applied to the two-dimensional Hubbard model. Employing the continuous-time quantum Monte Carlo method as the solver for the effective cluster model, we obtain
We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The technique i
We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity ap