Computer renormalization-group calculations of2kFand4kFcorrelation functions of the one-dimensional Hubbard model

We calculate $2k_F$ and $4k_F$ charge-density wave (CDW) and spin-density wave (SDW) autocorrelation functions for the one-dimensional Hubbard model using a computer renormalization-group technique previously developed by us. We describe the method and expected accuracy of the results. The correlation functions are calculated for Hubbard parameter $\frac{U}{t}=2,10,50\mathrm{}$ and for two different band fillings. We obtain, describe, and compare for the first time the magnitudes and temperature dependences of the correlation functions. We find, inter alia, that the $4k_F$ instability arises at very large $U$ and that the $2k_F$ SDW and $4k_F$ CDW dominate at large $U$.