Analysis of the dynamical cluster approximation for the Hubbard model

Details Analysis of the dynamical cluster approximation for the Hubbard model Analysis of the dynamical cluster approximation for the Hubbard model

2002-01-11

arxiv.org/abs/cond-mat/0201186v1

Physical. Review. B 65, 153102 (2002)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 6 figures. To appear in Phys. Rev. B as a Brief Report

Scientific paper

10.1103/PhysRevB.65.153102

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.

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