2pFand4pFinstabilities in a one-quarter-filled-band Hubbard model

The zero-frequency wave-vector-dependent charge- and spin-density susceptibilities for a quarter-filled-band extended Hubbard model are calculated with the use of a Monte Carlo technique. Results for a variety of different temperatures are given. Coulomb interactions are found to suppress the $2p_F$ charge-density response and enhance the $2p_F$ spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak $4p_F$ structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction $V$ in the extended Hubbard model can produce a singularity at $4p_F$. In addition to these susceptibilities, both the charge and spin structure factors are calculated, as well as two-particle, two-hole correlation functions. We also show some results for the ground-state energy, magnetic susceptibility, and specific heat of the Hubbard model. The relationship of the results obtained from our Monte Carlo simulations to various limiting exact results as well as to the well-known weak coupling renormalization-group predictions are discussed.