Spatial Correlations in Dynamical Mean Field Theory

TL;DR

This paper extends dynamical mean field theory by incorporating quantum fluctuations from intersite interactions, resulting in a momentum-dependent susceptibility while maintaining a local self-energy.

Contribution

It develops a new approach that includes intersite quantum fluctuations in DMFT, leading to momentum-dependent vertex functions and susceptibilities.

Findings

Two-particle vertex functions are momentum-dependent.

Single-particle self-energy remains local.

The approach is conserving despite momentum dependence.

Abstract

We further develop an extended dynamical mean field approach introduced earlier. It goes beyond the standard $D=\infty$ dynamical mean field theory by incorporating quantum fluctuations associated with intersite (RKKY-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 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.