Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference epsilon and the strength of the interaction beta. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility kappa. In particular kappa diverges on the boundary of the restricted region, indicating the occurrence of a phase transition.