Comparison of Monte Carlo and diagrammatic calculations for the two-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 8×8 lattice doped away from half filling were carried out down to temperatures of order 140 of the bandwidth. Results for the spin susceptibility χ(q,iω${}_{\mathrm{m}}$), the electron self-energy Σ(p,iω${}_{\mathrm{n}}$), various pair-field susceptibilities, and the irreducible particle-particle scattering vertex Γ(p′,iω${}_{\mathrm{n}\prime }$|p,iω${}_{\mathrm{n}}$) were obtained. A random-phase approximation for χ(q,iω${}_{\mathrm{m}}$) with a renormalized Coulomb coupling U¯ 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 Σ(p,iω${}_{\mathrm{n}}$) 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 Γ remain.