Localization versus delocalization in the one-dimensional Tomonaga model with impurities

We examine localization and delocalization in the one-dimensional Tomonaga model with impurities. We expand the density autocorrelation function in a perturbation series in the impurity coupling U_⊥. We then relate the terms in this series to the partition functions QN for an N-particle two-dimensional Coulomb gas. After obtaining new stringent bounds on QN, we use these bounds and the analytic properties of the perturbation series to predict localization. In contradiction of earlier results, we find that the electrons are localized (delocalized) for electron-electron interactions U_∥2πvF greater than (less than) -5/13, independent of U_⊥ vF is the Fermi velocity). This is the first time to our knowledge that a localization transition has been studied by such a bounded-series technique.