A NEW CLASS OF EXACTLY SOLVABLE INTERACTING FERMION MODELS IN ONE-DIMENSION

We investigate a model containing two species of one-dimensional fermi ons interacting via a gauge field determined by the positions of all p articles of the opposite species. The model can be salved exactly via a simple unitary transformation. Nevertheless, correlation functions e xhibit nontrivial interaction-dependent exponents. A similar model def ined on a lattice is introduced and solved. Various generalizations, e .g., to the case of internal symmetries of the fermions, are discussed . The present treatment also clarifies certain aspects of Luttinger's original solution of the ''Luttinger model.''