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Transport in Luttinger Liquids

T. Giamarchi·T. Nattermann·P. Le Doussal
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Abstract

We compute the transport properties of one dimensional interacting electrons, also known as a Luttinger liquid. We show that a renormalization group study allows to obtain the temperature dependence of the conductivity in an intermediate temperature range. In this range the conductivity has a power-law like dependence in temperature. At low temperatures, the motion proceed by tunnelling between localized configurations. We compute this tunnelling rate using a bosonization representation and an instanton technique. We find a conductivity $\sigma(T) \propto e^{-\beta^{1/2}}$, where $\beta$ is the temperature. We compare this results with the standard variable range hopping (VRH) formula.

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T. Giamarchi, T. Nattermann, P. Le Doussal. 2004-03-19. Transport in Luttinger Liquids. https://doi.org/10.1007/1-4020-2193-3_16

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