Computer renormalization-group calculations of the2kFand4kFcorrelation functions of an extended one-dimensional Hubbard model

We extend previous calculations of the $2k_F$ and $4k_F$ ($k_F\equiv \mathrm{Fermi}\mathrm{wave}\mathrm{vector}$) spin- and charge-density autocorrelation functions of the one-dimensional Hubbard model by including the nearest-neighbor Coulomb interaction $V$. The results are computed for finite chains containing up to eight sites using a computer renormalization-group technique previously developed by us. We find, inter alia, that the real part of the $4k_F$ charge-density wave (CDW), which is comparable to the real part of the $2k_F$ CDW when only large onsite Coulomb repulsion is considered, becomes greatly enhanced relative to the $2k_F$ CDW when $V$ is positive. This finding implies that the $V$ interaction is important in explaining the $4k_F$ instability of some quasi-one-dimensional materials.