1999/03/18 by M. H. Hettler, M. Mukherjee, M. Jarrell +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.61.12739
19 pages, 13 postscript figures, revtex
arxiv created 1999/03/18 · arxiv updated 2009/11/30
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.