Numerical study of the two-dimensional Hubbard model for various band fillings

Quantum Monte Carlo methods are used to study the physical properties of the two-dimensional Hubbard model for various band fillings. Results for the energy, magnetic moment, magnetic structure factor, and integrated optical spectral weight are presented. A comparison of the half-filled (〈n〉=1) and quarter-filled (〈n〉=0.5) bands is made using results for the momentum distribution 〈$n_k$〉, the compressibility K, and the one-electron self-energy Σ(k,i${\omega }_n$), which shows that a gap exists in the one-electron excitations at half-filling but is absent for the one-quarter-filled case. At a filling of 〈n〉=0.87, the locus of k values for which 〈$n_k$〉=0.5 is found to be close to the free Fermi surface for this filling.