Cluster Dynamical Mean Field Theories

Details Cluster Dynamical Mean Field Theories Cluster Dynamical Mean Field Theories

2003-07-23

arxiv.org/abs/cond-mat/0307587v1

Phys. Rev. B 69, 205108 (2004)

Physics

Condensed Matter

Strongly Correlated Electrons

26 pages

Scientific paper

10.1103/PhysRevB.69.205108

Cluster Dynamical Mean Field Theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean field theory, PCDMFT, is presented. The semiclassical limit of the cluster methods is analyzed by applying them to the Falikov-Kimball model in the limit of infinite Hubbard interaction U where they map to different classical cluster schemes for the Ising model. Furthermore the Cutkosky-t'Hooft-Veltman cutting equations are generalized and derived for non translation invariant systems using the Schwinger-Keldysh formalism. This provides a general setting to discuss causality properties of cluster methods. To illustrate the method, we prove that PCDMFT is causal while the nested cluster schemes (NCS) in general and the pair scheme in particular are not. Constraints on further extension of these schemes are discussed.

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