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

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 simplecubic lattice. We demonstrate how pseudogap formation in the many-body resonance at the Fermi level results from the inclusion of nonlocal correlations. A comparison of the spectral function with the dynamical-cluster approximation shows qualitative agreement of high-as well as low-energy features.

Realistic quantum critical point in one-dimensional two-impurity models

“…From a theoretical perspective, the two-impurity Anderson model (TIAM) [15][16][17] constitutes an important but simple system which embodies the competition of interactions between two localized magnetic moments with those between the impurities and the conduction band. The TIAM has been viewed as a paradigm model for the formation of two different singlet phases separated by a quantum critical point (QCP): a Ruderman-Kittel-Kasuya-Yosida (RKKY)-induced singlet and a Kondo singlet [15].…”