We provide microscopic diagrammatic derivations of the Molecular Coherent Potential Approximation (MCA) and Dynamical Cluster Approximation (DCA) and show that both are 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 O(1/Lc) (O(1/Lc^2)), where Lc is the linear size of the cluster. However, local quantities, when measured in the center of the MCA cluster, converge more quickly than the DCA result. These 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 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 O(1/Lc) (O(1/Lc^2)), where Lc is the linear size of the cluster. However, local quantities, when measured in the center of the MCA cluster, converge more quickly than the DCA result. These results are demonstrated numerically for the one-dimensional symmetric Falicov-Kimball model.

arXiv:cond-mat/0205460May 22, 20021 citation

Coherent-Potential Approximations

WORLD SCIENTIFIC eBooksOct 1, 20120 citations

Comparison of two-quantum-cluster approximations

Thomas Maier, Mark Jarrell

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

\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.