COMPARISON OF MONTE-CARLO AND DIAGRAMMATIC CALCULATIONS FOR THE 2-DIMENSIONAL HUBBARD-MODEL

Monte Carlo results for a two-dimensional Hubbard model in the intermediate-coupling regime U = 4t are compared with a diagrammatic spin-fluctuation approximation. Simulations on an 8 X 8 lattice doped away from half filling were carried out down to temperatures of order 1/40 of the bandwidth. Results for the spin susceptibility chi(q,iomega(m)), the electron self-energy SIGMA(p,iomega(n)), various pair-field susceptibilities, and the irreducible particle-particle scattering vertex GAMMA(p,iomega(n')\p,iomega(n)) were obtained. A random-phase approximation for chi(q,iomega(m)) with a renormalized Coulomb coupling UBAR is shown to provide a fit to the Monte Carlo data. A similar approximation for the Berk-Schrieffer spin-fluctuation interaction also provides a reasonable fit to the self-energy SIGMA(p,iomega(n)) in the region explored by the Monte Carlo data. However, a similar approximation for the irreducible particle-particle interaction failed to reproduce the Monte Carlo results. Higher-order vertex corrections were calculated, but significant discrepancies with Monte Carlo results for GAMMA remain.