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Electron-phonon interactions play a key role in many branches of solid-statephysics. Here, our focus is on the transport properties of one-dimensionalsystems, and we apply efficient real-time matrix-product state methods tocompute the optical and thermal conductivities of Holstein chains at finitetemperatures and filling. We validate our approach by comparison withanalytical results applicable to single polarons valid in the small polaronlimit. Our work provides a systematic study of contributions to the thermalconductivity at finite frequencies and elucidates differences in the spectrumcompared to the optical conductivity, covering both the Luttinger-liquid andcharge-density-wave regimes. Finally, we demonstrate that our approach iscapable of extracting the DC conductivities as well. Beyond this firstapplication, several future extensions seem feasible, such as, the inclusion ofdispersive phonons, different types of local electron-phonon coupling, and asystematic study of drag effects in this electron-phonon coupled system.

physical review. b./physical review. b

Thermal and optical conductivity in the Holstein model at half filling  and at finite temperature in the Luttinger-liquid and charge-density-wave  regime