Long-range interactions in a one-dimensional electron system
  We study the unscreened Coulomb interaction in a one-dimensional electron system at low-energy. We use renormalization group methods and a GW approximation, in order to analyze the model. This yields both a strong wavefunction renormalization and a renormalization of the Fermi velocity. The significance of the effects depends on the filling level of the Fermi system. Despite the long-range character of the interaction, the system still falls into the Luttinger liquid universality class, since the effective couplings remain bounded at arbitrarily low energies. 
S. Bellucci