Electroneutrality and the Friedel sum rule in a Luttinger liquid

Screening in one-dimensional metals is studied for arbitrary electron-electron interactions. It is shown that for finite-range interactions (Luttinger liquid) electroneutrality is violated. This apparent inconsistency can be traced to the presence of external screening gates responsible for the effectively short-ranged Coulomb interactions. We also draw attention to the breakdown of linear screening for wave vectors close to 2k(F).