Single-barrier problem and Anderson localization in a one-dimensional interacting electron system

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Abstract
Transport through a single barrier in a one-dimensional (1D) interacting electron system is studied theoretically. By using renormalization group and duality mapping, the phase diagram of the ground state is shown to be divided into four regions in terms of the zero-temperature limits of the charge and spin conductances. The conductances are calculated perturbatively for both limits of weak and strong potential. The results are applied to clarify the crossover and scaling of the Anderson localization in a 1D system with dilute impurities. It is shown that the temperature dependence of the resistivity of the system can change significantly around a characteristic temperature corresponding to discretization energy.