Exact distribution function of a one-dimensional Fro¨hlich-Toyozawa-Luttinger liquid

An exact analytical expression for the electron momentum distribution function of a one-dimensional Frohlich-Toyozawa-Luttinger (FTL) liquid is obtained. It is explicitly shown that the residual Fermi surface disappears when the electron-electron interaction is increased. It is furthermore shown that the electron-phonon interactions also flatten the distribution function, the optical phonons having a larger effect than the acoustic phonons. However, it is found that the nature of the distribution function of an FTL liquid is qualitatively different from that of the corresponding Luttinger liquid above kF.