Thermal Transport in a Luttinger Liquid

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 Wiedemann-Franz law—is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorentz number is given by $L(T\to 0){=3L}_0/\left({2g+g}^2\right)$—with $L_0$ the Fermi liquid value—and the conductance $1/2<g<\mathrm{}1\mathrm{}$. For $g<\mathrm{}1\mathrm{}/2$ the Lorentz number diverges as $T\to 0$. Possible relevance to thermal transport in conducting polymer systems is discussed.