Cluster Dynamical Mean Field Theories

Abstract

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.

26 pages

References in corpus (3)

• First principles approach to the electronic structure of strongly correlated systems: combining GW and DMFT
• Cellular Dynamical Mean Field Theory for the 1D Extended Hubbard Model
• Fictive Impurity Models: an Alternative Formulation of the Cluster Dynamical Mean Field Method

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