Dynamic response of one-dimensional interacting fermions

We evaluate the dynamic structure factor S(q,omega) 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,omega). The sharp peak S(q,omega)proportional to q delta(omega-uq), characteristic for the Tomonaga-Luttinger model, broadens up; S(q,omega) for a fixed q becomes finite at arbitrarily large omega. The main spectral weight, however, is confined to a narrow frequency interval of the width delta omega similar to 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.