Flux quantization in the two-dimensional repulsive and attractive Hubbard models

In order to provide a numerical criterion for superconductivity, the ground state energy ${\mathit{E}}_0$(Φ) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux Φ. From the functional form of ${\mathit{E}}_0$(Φ), superconducting ground states may be identified without prior knowledge of the pairing symmetry. ${\mathit{E}}_0$(Φ) 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.