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). · 3.66 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). · 3.66 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We apply a recently introduced hybridization flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard model on the Bethe lattice in infinite dimensions we calculate the local two-particle vertex for the metallic and the insulating phase. Then we go to a two-site cluster DMFT scheme for the two-dimensional Hubbard model that includes short-range antiferromagnetic fluctuations and obtain the local and nonlocal two-particle vertex functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.Physical Review B 11/2013; 88(19). · 3.66 Impact Factor

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