Abstract
Schulz and Shastry recently introduced a new class of exactly solvable one-dimensional models with non-Fermi-liquid physics. First, we show that this behavior is caused by the existence of anyonic excitations (i.e. states with non-trivial conformal spin) with charge [(δ)/(2π)], where δ is the phase shift of the potential. Since δ is an arbitrary real number, these anyons may therefore carry an irrational charge. Next, in view of this result we revisit the general classification of non-Fermi-liquid two-species gapless 1D models: while it is usually thought that c = 1 × c = 1 theories form a four-parameter space, we establish that the most general non-relativistic conformal field theory has ten parameters. This defines a single larger universality class with sub-manifolds associated with the standard Luttinger liquid (with spin-charge separation), and the Schulz-Shastry class of models.