In order to provide a numerical criterion for superconductivity, the ground state energy ${\mathit{E}}_{0}$ (\ensuremath{\Phi}) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux \ensuremath{\Phi}. From the functional form of ${\mathit{E}}_{0}$ (\ensuremath{\Phi}), superconducting ground states may be identified without prior knowledge of the pairing symmetry. ${\mathit{E}}_{0}$ (\ensuremath{\Phi}) is calculated with Monte Carlo methods. For the attractive Hubbard model, our results confirm the existence of a superconducting ground state. In contrast, our results show that the quarter-filled repulsive Hubbard model is not superconducting and that a Hartree-Fock paramagnetic approximation fits the data very well.In order to provide a numerical criterion for superconductivity, the ground state energy ${\mathit{E}}_{0}$(\ensuremath{\Phi}) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux \ensuremath{\Phi}. From the functional form of ${\mathit{E}}_{0}$(\ensuremath{\Phi}), superconducting ground states may be identified without prior knowledge of the pairing symmetry. ${\mathit{E}}_{0}$(\ensuremath{\Phi}) is calculated with Monte Carlo methods. For the attractive Hubbard model, our results confirm the existence of a superconducting ground state. In contrast, our results show that the quarter-filled repulsive Hubbard model is not superconducting and that a Hartree-Fock paramagnetic approximation fits the data very well.

Physical Review LettersSep 20, 199335 citations

Magnetic and superconductive states in the repulsive Hubbard model

Victor Nikolaevich Popov

Journal of Mathematical SciencesJun 1, 19973 citations

Anisotropic superconductivity in the two-dimensional Hubbard model

Marcin Mierzejewski, J. Zieliński

We address the problem of superconductivity in a system where the only many-body interactions are repulsive. The Eliashberg equations have been generalized to account for possible pairing correlations in the two-dimensional Hubbard model. Details of the two-dimensional band structure have been explicitly taken into account when considering the symmetry of the superconducting state. The pairing kernels have been discussed at low doping and at temperatures close to the superconducting transition temperature. We have proved that local Coulomb repulsion leads to attractive pairing correlations in the $d$ -wave channel. Extended $s$ -wave superconductivity is less likely to occur within this purely electronic model, at least in the physically interesting region of doping.We address the problem of superconductivity in a system where the only many-body interactions are repulsive. The Eliashberg equations have been generalized to account for possible pairing correlations in the two-dimensional Hubbard model. Details of the two-dimensional band structure have been explicitly taken into account when considering the symmetry of the superconducting state. The pairing kernels have been discussed at low doping and at temperatures close to the superconducting transition temperature. We have proved that local Coulomb repulsion leads to attractive pairing correlations in the $d$-wave channel. Extended $s$-wave superconductivity is less likely to occur within this purely electronic model, at least in the physically interesting region of doping.

Physical review. B, Condensed matterNov 1, 199717 citations

Superconductivity in the Repulsive Hubbard Model

D. Baeriswyl

Journal of Superconductivity and Novel MagnetismDec 21, 201015 citations

In order to provide a numerical criterion for superconductivity, the ground state energy

{\mathit{E}}_{0}

(\ensuremath{\Phi}) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux \ensuremath{\Phi}. From the functional form of

{\mathit{E}}_{0}

(\ensuremath{\Phi}), superconducting ground states may be identified without prior knowledge of the pairing symmetry.

{\mathit{E}}_{0}

(\ensuremath{\Phi}) is calculated with Monte Carlo methods. For the attractive Hubbard model, our results confirm the existence of a superconducting ground state. In contrast, our results show that the quarter-filled repulsive Hubbard model is not superconducting and that a Hartree-Fock paramagnetic approximation fits the data very well.

d

-wave channel. Extended

s

-wave superconductivity is less likely to occur within this purely electronic model, at least in the physically interesting region of doping.