Spatial correlations in dynamical mean-field theory

We further develop an extended dynamical mean-field approach introduced earlier. It goes beyond the standard D=∞ dynamical mean field theory by incorporating quantum fluctuations associated with intersite (Ruderman-Kittel-Kasuya-Yosida like) interactions. This is achieved by scaling the intersite interactions to the same power in $1/D$ as that for the kinetic terms. In this approach, a correlated lattice problem is reduced to a single-impurity Anderson model with additional self-consistent bosonic baths. Here, we formulate the approach in terms of standard perturbation expansions. We show that the two-particle vertex functions are momentum-dependent, while the single-particle self-energy remains local. In spite of this, the approach is conserving. Finally, we also determine the form of a momentum-dependent dynamical susceptibility; the resulting expression relates it to the corresponding Weiss field, local correlation function and (momentum-dependent) intersite coupling.