Influence of the electron-electron interaction on electronic spectra and persistent currents in one-dimensional loops

We consider N electrons in a one-dimensional loop enclosing a static magnetic flux. The electronic positions are described in terms of collective and relative coordinates. The corresponding partition of the Hilbert space is particularly convenient to investigate the electronic spectrum in the range of large electron-electron interaction. The electronic current is determined by the collective motion of the electrons. Thus, in absence of backscattering by a one-particle potential, the electron-electron interaction does not affect the persistent current associated with the electronic ground state. This is different when backscattering is present, since then collective and relative motions are coupled. We present a detailed study of the interplay between potential backscattering and electron-electron interaction, which is revealed by the resulting ground-state currents as well as by the electronic excitation spectra.