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In recent experiments on conductance of one-dimensional (1D) channels inultra-clean samples, a diverse set of plateaus were found at fractions of thequantum of conductance in zero magnetic field. We consider a discrete model ofstrongly interacting electrons in a clean 1D system where the current betweenweak tunneling contacts is carried by fractionally charged solutions. While inthe spinless case conductance remains unaffected by the interaction, as istypical for the strongly interacting clean 1D systems, we demonstrate that inthe spinful case the peak conductance takes fractional values that depend onthe filling factor of the 1D channel.

Resonant fractional conductance through a 1D Wigner chain