SPECTRAL PROPERTIES AND SUM-RULES OF THE ONE-DIMENSIONAL HUBBARD-MODEL

We study spectral properties of dynamical structure factors of the one-dimensional Hubbard model at T = 0, using sum rules and the Bethe-ansatz solution. Sum rules help us to obtain information about dynamic quantities from static quantities. We estimate the spectral weight on the lowest-excitation frequency in the dynamical structure factors of spin and charge at small momenta. It is found that there exists a strong or broad continuum spectrum at small momentum above the lowest frequency in the dynamical spin-structure factor of the dilute limit and in the dynamical charge-structure factor near half filling. The spectral weight on the lowest frequency is negligible in these two regions. In other regions, most of the spectral weight concentrates near the lowest frequency.