ferromagnetic transition in chiral metal

This letter studies a spinful 1D chiral electron model with contact interaction and nonlinear dispersion, where an itinerant ferromagnetic phase transition happens at repulsive interaction and an Amperean pairing at attractive interaction, the two phases are symmetrical and connected by a particle-hole transformation. We use bosonization and relate it with the fermion model to study the phase transition criticality and find the spin and charge modes have different dynamical exponent, which leads to a fractional-power time correlation, unlike the Luttinger liquid theory. We also find a similar transition in the quantum Hall edge states, the nonlinear dispersion is replaced with the presence of interaction form factor after projecting to the Landau levels.