We study one-dimensional clean systems with few channels and strong electron-electron interactions. We find that in several circumstances, even when time-reversal symmetry holds, they may lead to two-terminal fractional quantized conductance and fractional shot noise. The condition on the commensurability of the Fermi momenta of the different channels and the strength of the interactions resulting in such remarkable phenomena are explored in two scenarios: (i) strong repulsive interactions, and (ii) spatially modulated attractive interactions. Finite temperature and length effects may be accurately accounted for by a generalization of the Luther-Emery refermionization at specific values of the interaction strength, deep in the strongly interacting regime. We further discuss how at very small energy scales the conductance returns to an integer value and consider also the role of disorder. We discuss the connection of our model to recent experiments in a confined two-dimensional electron gas and oxide interface wires, featuring possible fractional conductance plateaus, including situations with a zero magnetic field. Two of the most dominant observed fractions, 2/5 and 9/5 of the quantum of conductance, are featured prominently in our model.

[1] G. Shavit and Y. Oreg, Fractional conductance in strongly interacting 1d systems, Phys. Rev. Lett.123, 036803 (2019).