Unscreened Coulomb repulsion in the one-dimensional electron gas

A tight-binding model of electrons interacting via bare Coulomb repulsion is numerically investigated by use of the density-matrix renormalization group method which we prove applicable also to very long-range potentials. From the analysis of the elementary excitations, of the spin and charge correlation functions, and of the momentum distribution, a picture consistent with the formation of a one-dimensional ``Wigner crystal'' emerges, in quantitative agreement with a previous bosonization study. At finite doping, umklapp scattering is shown to be ineffective in the presence of long-range forces.