Breakdown of the chiral Luttinger liquid in one dimension

We have developed a fermionic boot-strap method to solve a class of chiral one-dimensional fermion models. Using this scheme, we show that Luttinger liquid behavior in a gas of four interacting chiral Majorana fermions is highly sensitive to the velocity degeneracy. Upon changing the velocity of one chiral fermion, a sharp bound (or antibound) state splits off from the original Luttinger liquid continuum, cutting off the x-ray singularity to form a broad incoherent excitation with a lifetime that grows linearly with frequency