Dynamical Cluster Approximation Employing FLEX as a Cluster Solver

Details Dynamical Cluster Approximation Employing FLEX as a Cluster Solver Dynamical Cluster Approximation Employing FLEX as a Cluster Solver

2002-09-06

arxiv.org/abs/cond-mat/0209170v2

Physical. Review. B 67, 085101 (2003)

Physics

Condensed Matter

Strongly Correlated Electrons

15 pages, 24 figures. Submitted to Physical Review B as a Regular Article

Scientific paper

10.1103/PhysRevB.67.085101

We employ the Dynamical Cluster Approximation (DCA) in conjunction with the Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA is a technique to systematically restore the momentum conservation at the internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which classes of Feynman diagrams are summed over analytically using geometric series. The FLEX is used as a tool to investigate the complementarity of the DCA and the finite size lattice technique with periodic boundary conditions by comparing their results for the Hubbard model. We also study the microscopic theory underlying the DCA in terms of compact (skeletal) and non-compact diagrammatic contributions to the thermodynamic potential independent of a specific model. The significant advantages of the DCA implementation in momentum space suggests the development of the same formalism for the frequency space. However, we show that such a formalism for the Matsubara frequencies at finite temperatures leads to acausal results and is not viable. However, a real frequency approach is shown to be feasible.

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