2pFand4pFInstabilities in the One-Dimensional Electron Gas

Charge- and spin-density response functions in the one-dimensional ¼-filled extended Hubbard model have been studied by use of a Monte Carlo technique. The results show that Coulomb interactions suppress the $2p_{\mathrm{F}}$ charge-density singularity, while they enhance the $2p_{\mathrm{F}}$ spin-density singularity. The $4p_{\mathrm{F}}$ response is only appreciable if, in addition to on-site repulsion, longer-range interactions exist. The present results are compared with weak-coupling renormalization-group predictions.