The Ground and Low Lying Excited States of the Two-Dimensional Hubbard Model

We have studied the ground state of the two-dimensional (2D) Hubbard model by using a quantum monte method paying special attention to the shell structure effect on finite size clusters. Our calculations show there is a gap for spin excitations in the ground state and incommensurate peaks at $(\pi \pm \delta, \pi)$ and $(\pi, \pi \pm \delta)$ in the spin correlation function for a low lying excited state. In the ground state, the long range part of the d-wave superconducting correlation function is enhanced and the momentum distribution function at the Fermi level $(\pi,0)$ is rounded. The gap in spin excitations and the momentum distribution function rounding is consistent with opening a d-wave superconducting gap in the ground state.