Dynamic Response of One-Dimensional Interacting Fermions

We evaluate the dynamic structure factor S (q, ) of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of S (q, ). The sharp peak S (q, ) (-uq), characteristic for the Tomonaga-Luttinger model, broadens up; S (q, ) for a fixed q becomes finite at arbitrarily large. The main spectral weight, however, is confined to a narrow frequency interval of the width q^2/m. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number q.