Charge-spin separation and the spectral properties of Luttinger liquids

We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between vsigma q and vrho q, where vsigma and vrho are the velocities of spin and charge fluctuations, while spectral weight above vrho q and below -vrho q is generated by the hybridization of the Fermi surface at +or-kF by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.