Article

# Critical properties of the half-filled Hubbard model in three dimensions.

Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria.

Physical Review Letters (Impact Factor: 7.73). 12/2011; 107(25):256402. DOI: 10.1103/PhysRevLett.107.256402 Source: PubMed

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**ABSTRACT:**We present an 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 [under 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. A comparison of the spectral function with the dynamical-cluster approximation shows qualitative agreement of high- as well as low-energy features.Physical review. B, Condensed matter 04/2012; 85(16). · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length scales beyond the local correlations of dynamical mean-field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (DΓA) and the dual fermion (DF) scheme, yielding a consistent formulation of nonlocal correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of DΓA. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF, and DΓA, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.Physical review. B, Condensed matter 09/2013; 88(11). · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a novel scheme for an unbiased and non-perturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, i.e., the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). Physically, this allows for a systematic inclusion of non-local correlations via the flow equations of the fRG, after the local correlations are taken into account non-perturbatively by the DMFT. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half-filling.Physical Review Letters 07/2013; · 7.73 Impact Factor

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