Berlin 2005 – scientific programme
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TT: Tiefe Temperaturen
TT 7: Correlated Electrons - (General) Theory II
TT 7.1: Invited Talk
Friday, March 4, 2005, 16:30–17:00, TU H2053
Self-Energy Functionals: A New Approach to Strongly Correlated Electron Systems — •Michael Potthoff — Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Germany
Since the seminal work by Luttinger, Ward, Baym and Kadanoff in the sixties, we know about a fundamental variational principle of the form δ Ω[Σ]=0. This is interesting as it promises an access to the grand potential Ω and the self-energy Σ for a system of interacting fermions and, thereby, to the equilibrium thermodynamics as well as to (one-particle) excitations. While truncations of the functional form were frequently used in the past to construct weak-coupling (“conserving”) approximations, it is surprising that there has not been a single direct application of the variational principle until recently. This stands in marked contrast to the widespread Ritz principle δ E[Ψ]=0 which, however, does not give information on excitation properties.
This talk shows how to make use of the Luttinger-Ward variational principle in various physical situations. In the high-Tc problem, for example, systematic and non-perturbative approaches are needed which accurately treat short-range correlations while directly working in the thermodynamic limit. This can be achieved with a novel variational cluster-perturbation theory. Contacts can be made to the cluster generalizations of the DMFT. For various transition metals and oxides, on the other hand, a local (mean-field) approximation is sufficient. Here the self-energy-functional approach shows up an efficient way to account for the temporal degrees of freedom. Extensions of the method to include phonons, non-local interactions and to disordered systems are discussed.