Extension of dynamical mean-field theory by inclusion of nonlocal two-site correlations with variable distance

TL;DR

This paper introduces an advanced method extending dynamical mean-field theory to incorporate nonlocal two-site correlations at variable distances, enabling more accurate modeling of strongly correlated electrons in complex lattices.

Contribution

The authors develop a new approximation scheme that includes nonlocal two-site correlations of arbitrary spatial extent within dynamical mean-field theory, respecting translational invariance.

Findings

Demonstrated pseudogap formation due to nonlocal correlations in the 2D Hubbard model.

Extended DMFT captures spatially extended correlations beyond local interactions.

Method applicable to arbitrary crystal lattices with variable correlation distances.

Abstract

We present a novel approximation scheme for the treatment of strongly correlated electrons in arbitrary crystal lattices. The approach extends the well-known dynamical mean field theory to include nonlocal two-site correlations of arbitrary spatial extent. We extract the nonlocal correlation functions from two-impurity Anderson models where the impurity-impurity distance defines the spatial extent of the correlations included. Translational invariance is fully respected by our approach since correlation functions of any two-impurity cluster are periodically embedded to $k$-space via a Fourier transform. As a first application, we study the two-dimensional Hubbard model on a simple-cubic lattice. We demonstrate how pseudogap formation in the many-body resonance at the Fermi level results from the inclusion of nonlocal correlations.