Strong coupling theory for interacting lattice models

We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this analysis is twofold: (1) It provides the tools for a unified treatment of any nonlocal contribution to the Hamiltonian. Within our scheme, nonlocal terms such as hopping terms, spin-spin interactions, or nonlocal Coulomb interactions are treated on equal footing. (2) By performing a detailed strong-coupling analysis of a generalized lattice problem, we establish the basis for possible clean and systematic extensions beyond DMFT. To this end, we study the problem using three different perspectives. First, we develop a generalized expansion around the atomic limit in terms of the coupling constants for the nonlocal contributions to the Hamiltonian. By analyzing the diagrammatics associated with this expansion, we establish the equations for a generalized dynamical mean-field theory. Second, we formulate the theory in terms of a generalized strong coupling version of the Baym-Kadanoff functional. Third, following Pairault, Senechal, and Tremblay [Phys. Rev. Lett. 80, 5389 (1998)], we present our scheme in the language of a perturbation theory for canonical fermionic and bosonic fields and we establish the interpretation of various strong coupling quantities within a standard perturbative picture.