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

TL;DR

The paper introduces the dynamical cluster approximation (DCA), a new method for including short-range dynamical correlations in electron systems, demonstrating its effectiveness and convergence in a 2D model.

Contribution

It presents the DCA as a causal, systematic, and conserving technique that extends dynamical mean field theory by incorporating non-local correlations.

Findings

Spectral functions preserve causality.

Spectra and transition temperatures converge with increasing cluster size.

Method is validated on the 2D Falicov-Kimball model.

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.