Thermal transport in a Luttinger liquid

Abstract

We study thermal transport in a one-dimensional (1d) interacting electron gas, employing the Luttinger liquid model. Both thermal conductance and thermopower are analyzed for a pure 1d gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi-liquid - the Wiedeman-Franz law - is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorenz number is given by $L(T\to 0)=3L_0/(2g+g^2)$ - with $L_0$ the Fermi liquid value - and the conductance $1/2<g<1$. For $g<1/2$ the Lorenz number {\it diverges} as $T\to 0$. Possible relevance to thermal transport in conducting polymer systems is discussed.

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