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 wavevectors close to 2 K_f.