FLUX-QUANTIZATION IN THE 2-DIMENSIONAL REPULSIVE AND ATTRACTIVE HUBBARD MODELS

In order to provide a numerical criterion for superconductivity, the ground state energy E0(PHI) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux PHI. From the functional form of E0(PHI), superconducting ground states may be identified without prior knowledge of the pairing symmetry. E0(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.