  Recent ultracold atomic gas experiments implementing synthetic spin-orbit
coupling allow access to flatbands that emphasize interactions. We model
spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We
introduce an effective Luttinger-liquid theory to show that interactions
generate collective excitations with emergent kinetics and fractionalized
charge, analogous to properties found in the two-dimensional fractional quantum
Hall regime. Observation of these excitations would provide an important
platform for exploring exotic quantum states derived solely from interactions.
