The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems

Abstract

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 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, $\Phi$-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 CDW transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

19 pages, 13 postscript figures, revtex

References in corpus (3)

• Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
• Spatial Correlations in Dynamical Mean Field Theory
• Comment on "Robustness of a Local Fermi Liquid against Ferromagnetism and Phase Separation"

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