Quantum fluctuations in the one dimensional Hubbard model with a less than half filling

The electronic structure of the one dimensional Hubbard model with a less than half filling is studied by the resonating Hartree-Fock (Res HF) method. For the Hubbard ring with 16 sites, the Res HF wave function composed of only 6 Slater determinants can explain at most 98.6% (14 electrons) and 99.4% (10 electrons) of the exact correlation energy. The spin structure factor in the Res HF ground state has a cusp at Q = 2pF, which is consistent with the previous quantum Monte CArlo result.