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 show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact graphs should be inferred from the appropriate Dyson equation. The distinction between non-compact and compact diagrams persists even in the limit of infinite dimensions. Non-local corrections beyond the DCA exist for the non-compact diagrams, whereas they vanish for compact diagrams.
@article{arxiv.cond-mat/0201186,
title = {Analysis of the dynamical cluster approximation for the Hubbard model},
author = {K. Aryanpour and M. H. Hettler and M. Jarrell},
journal= {arXiv preprint arXiv:cond-mat/0201186},
year = {2009}
}
Comments
4 pages, 6 figures. To appear in Phys. Rev. B as a Brief Report