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

M. H. Hettler·M. Mukherjee·M. Jarrell·H. R. Krishnamurthy
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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, $Φ$-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.

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M. H. Hettler, M. Mukherjee, M. Jarrell, H. R. Krishnamurthy. 1999-03-18. The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems. https://doi.org/10.1103/physrevb.61.12739

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