We apply the homomorphic cluster coherent potential approximation (HCPA) to systems with site-diagonal and/or off-diagonal randomness. We show numerically that the average Green's function obtained on the basis of the HCPA is analytic off the real axis on the complex energy plane. We also show that the HCPA reproduces the ordinary single-site CPA and the molecular CPA when systems include only diagonal disorder. The HCPA is advantageous in that it can deal with both site-diagonal and off-diagonal disorder in a unified manner. We also present a numerical result for a disordered chain by taking both kinds of disorder into account. The density of states calculated in the HCPA is in good agreement with the result of a computer simulation.We apply the homomorphic cluster coherent potential approximation (HCPA) to systems with site-diagonal and/or off-diagonal randomness. We show numerically that the average Green's function obtained on the basis of the HCPA is analytic off the real axis on the complex energy plane. We also show that the HCPA reproduces the ordinary single-site CPA and the molecular CPA when systems include only diagonal disorder. The HCPA is advantageous in that it can deal with both site-diagonal and off-diagonal disorder in a unified manner. We also present a numerical result for a disordered chain by taking both kinds of disorder into account. The density of states calculated in the HCPA is in good agreement with the result of a computer simulation.

Journal of the Physical Society of JapanAug 15, 197915 citations

Coherent states for general potentials

A. D. Jannussis, V. Papatheou, N. Patargias +1 more

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJul 1, 19818 citations

Realistic One-Dimensional Potentials

D. Baye, M. Dufour, Benjamin Fuks E

UNITEXT for physicsJan 1, 20250 citations

Two Quantum Cluster Approximations

Thomas Maier, O. Gonzalez, M. Jarrell +1 more

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

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.