Publication : t03/105

Cluster dynamical mean-field theories: Causality and classical limit

Biroli G. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Parcollet O. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Kotliar G. (Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA)
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.
Année de publication : 2004
Revue : Phys. Rev. B 69 205108 (2004)
DOI : 10.1103/PhysRevB.69.205108
Preprint : arXiv:cond-mat/0307587
Lien : http://link.aps.org/abstract/PRB/v69/p205108
PACS : 71.10.-w, 71.30.+h
Langue : Anglais

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