A diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it therefore becomes possible to treat the irreducible vertices of an effective single-impurity problem as small parameters. This provides a very efficient interpolation between weak coupling (band) and atomic limits. The antiferromagnetic pseudogap formation in the Hubbard model is correctly reproduced by just the lowest-order diagrams.A diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it therefore becomes possible to treat the irreducible vertices of an effective single-impurity problem as small parameters. This provides a very efficient interpolation between weak coupling (band) and atomic limits. The antiferromagnetic pseudogap formation in the Hubbard model is correctly reproduced by just the lowest-order diagrams.

arXiv:cond-mat/0612196Physical Review BJan 11, 2008350 citations

Correlation effects in the Hubbard model

Jakob Bernasconi

The European Physical Journal BJul 1, 19725 citations

Ferromagnetism and nonlocal correlations in the Hubbard model

Stefan W. Henning, Wolfgang Nolting

We study the possibility and stability of band ferromagnetism in the single-band Hubbard model for the simple cubic (sc) lattice. A nonlocal self-energy is derived within a modified perturbation theory. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of $\mathbf{k}$ dependence. The importance of nonlocal correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase diagram showing regions of ferromagnetic order is calculated for the three-dimensional lattice. Besides, we show results for the optical conductivity and prove that the renormalized one-loop contribution to the conductivity already cancels the Drude peak exactly in case of a local self-energy which is not true anymore for a nonlocal self-energy.We study the possibility and stability of band ferromagnetism in the single-band Hubbard model for the simple cubic (sc) lattice. A nonlocal self-energy is derived within a modified perturbation theory. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of $\mathbf{k}$ dependence. The importance of nonlocal correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase diagram showing regions of ferromagnetic order is calculated for the three-dimensional lattice. Besides, we show results for the optical conductivity and prove that the renormalized one-loop contribution to the conductivity already cancels the Drude peak exactly in case of a local self-energy which is not true anymore for a nonlocal self-energy.

arXiv:1203.1726Physical Review BMar 16, 20121 citation

Correlation effects in the extended Hubbard model

Ryszard Taranko, E. Taranko

Physica B Condensed MatterOct 1, 19884 citations

\mathbf{k}

dependence. The importance of nonlocal correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase diagram showing regions of ferromagnetic order is calculated for the three-dimensional lattice. Besides, we show results for the optical conductivity and prove that the renormalized one-loop contribution to the conductivity already cancels the Drude peak exactly in case of a local self-energy which is not true anymore for a nonlocal self-energy.