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Dynamical Response Function of 2 {\mib k}\sbf F-SDW for the Tomonaga-Luttinger Model

The response function, χ R SDW ( q ,ω), of 2 k F -SDW (spin density wave) with momentum 2 k F + q and frequency ω has been studied for the Tomonaga-Luttinger model by taking account of the momentum cutoff of the repulsive interaction where k F is the Fermi momentum. We have found that Im χ R SDW ( q ,ω) as a function of ω exhibits a novel peak located at an energy with the Fermi velocity, in addition to two peaks at energies with the renormalized velocities, v ρ and v σ corresponding to charge and spin excitations. Temperature dependence of Im χ R SDW ( q ,ω) is calculated to show that the spin fluctuation is dominant at low temperatures for the strong interaction and that the peak vanishes at high temperatures leading to a crossover into that in the absence of interaction.