Two Quantum Cluster Approximations

Details Two Quantum Cluster Approximations Two Quantum Cluster Approximations

2002-05-22

arxiv.org/abs/cond-mat/0205460v1

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, 6 figures; to be published in proceedings of the XV Workshop on Recent Developments in Computer Simulation Studies i

Scientific paper

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.

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