We provide microscopic diagrammatic derivations of the molecular coherent potential approximation (MCA) and dynamical cluster approximation (DCA) and show that both are $\ensuremath{\Phi}$ derivable. The MCA (DCA) maps the lattice onto a self-consistently embedded cluster with open (periodic) boundary conditions, and therefore violates (preserves) the translational symmetry of the original lattice. As a consequence of the boundary conditions, the MCA (DCA) converges slowly (quickly) with corrections $\mathcal{O}{(1/L}_{c})$ $[\mathcal{O}{(1/L}_{c}^{2})],$ where ${L}_{c}$ is the linear size of the cluster. These analytical results are demonstrated numerically for the one-dimensional symmetric Falicov-Kimball model.We provide microscopic diagrammatic derivations of the molecular coherent potential approximation (MCA) and dynamical cluster approximation (DCA) and show that both are $\ensuremath{\Phi}$ derivable. The MCA (DCA) maps the lattice onto a self-consistently embedded cluster with open (periodic) boundary conditions, and therefore violates (preserves) the translational symmetry of the original lattice. As a consequence of the boundary conditions, the MCA (DCA) converges slowly (quickly) with corrections $\mathcal{O}{(1/L}_{c})$ $[\mathcal{O}{(1/L}_{c}^{2})],$ where ${L}_{c}$ is the linear size of the cluster. These analytical results are demonstrated numerically for the one-dimensional symmetric Falicov-Kimball model.

arXiv:cond-mat/0110192Physical review. B, Condensed matterJan 3, 200225 citations

The Dynamical Cluster Approximation: A Microscopic Theory for the Cuprates

Thomas Maier

APSMar 1, 20010 citations

Analysis of the dynamical cluster approximation for the Hubbard model

Karan Aryanpour, Matthias H. Hettler, Mark Jarrell

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 noncompact and compact contributions to the thermodynamic potential. We show that approximating noncompact 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 noncompact graphs should be inferred from the appropriate Dyson equation. The distinction between noncompact and compact diagrams persists even in the limit of infinite dimensions. Nonlocal corrections beyond the DCA exist for the noncompact diagrams, whereas they vanish for compact diagrams.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 noncompact and compact contributions to the thermodynamic potential. We show that approximating noncompact 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 noncompact graphs should be inferred from the appropriate Dyson equation. The distinction between noncompact and compact diagrams persists even in the limit of infinite dimensions. Nonlocal corrections beyond the DCA exist for the noncompact diagrams, whereas they vanish for compact diagrams.

arXiv:cond-mat/0201186Physical review. B, Condensed matterMar 29, 200216 citations

\mathcal{O}{(1/L}_{c})

[\mathcal{O}{(1/L}_{c}^{2})],

where

{L}_{c}

is the linear size of the cluster. These analytical results are demonstrated numerically for the one-dimensional symmetric Falicov-Kimball model.