We use the dynamical vertex approximation $(\text{D}\ensuremath{\Gamma}\text{A})$ with a Moriyaesque $\ensuremath{\lambda}$ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The $\mathbf{k}$ dependence of the self-energy appears to be also much more pronounced in two dimensions as can be observed in the $\mathbf{k}$ -resolved $\text{D}\ensuremath{\Gamma}\text{A}$ spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.We use the dynamical vertex approximation $(\text{D}\ensuremath{\Gamma}\text{A})$ with a Moriyaesque $\ensuremath{\lambda}$ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The $\mathbf{k}$ dependence of the self-energy appears to be also much more pronounced in two dimensions as can be observed in the $\mathbf{k}$-resolved $\text{D}\ensuremath{\Gamma}\text{A}$ spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.

arXiv:0808.0689Physical Review BAug 5, 2009146 citations

Symmetry breaking in the Hubbard model at weak coupling

T. Schauerte, P. G. J. van Dongen

The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the N\'eel temperature and the order parameter in $d=3$ are smaller than the Hartree-Fock predictions by a factor of $q=0.2599.$ For $d=2$ we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters.The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the N\'eel temperature and the order parameter in $d=3$ are smaller than the Hartree-Fock predictions by a factor of $q=0.2599.$ For $d=2$ we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters.

arXiv:cond-mat/0202492Physical review. B, Condensed matterFeb 7, 200215 citations

\mathbf{k}

dependence of the self-energy appears to be also much more pronounced in two dimensions as can be observed in the

\mathbf{k}

-resolved $\text{D}\ensuremath{\Gamma}\text{A}$ spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.

The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the N\'eel temperature and the order parameter in

d=3

are smaller than the Hartree-Fock predictions by a factor of

q=0.2599.

For

d=2

we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters.