Stable 1d non-Fermi liquids and lattice theory

We show that a one-dimensional quantum wire with as few as 2 channels of interacting fermions can host gapless Luttinger liquid phases that are stable against nearly all perturbations. In particular, weak disorder does not lead to localization, a weak periodic potential fails to open a gap, and contact with a superconductor also fails to open a gap. The existence of these fixed points is related to questions in lattice theory, and their stability is due to strong (but not fine-tuned) competing attractive and repulsive interactions between the channels. The leading relevant perturbations, when they are present, are complicated operators that are expected to modify the physics only at very low energies (possibly below accessible temperatures). We propose physical realizations of these phases.