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 $U_{\perp }$. We then relate the terms in this series to the partition functions $Q_N$ for an $N$-particle two-dimensional Coulomb gas. After obtaining new stringent bounds on $Q_N$, 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 $\frac{U_{\parallel }}{2\pi v_F}$ greater than (less than) -5/13, independent of $U_{\perp }$ $v_F$ 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.