LUTTINGER LIQUID IN A SOLVABLE 2-DIMENSIONAL MODEL

We consider spinless electrons in two dimensions with the bare spectru m epsilon(p) = v(F)(\p(z)\ + \p(y)\). In momentum space, the interacti ons among electrons have a finite range q(0), which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifet ime indicates a breakdown of Landau's Fermi-Liquid theory in the model . At the one-loop level of perturbation theory, we show that the densi ty wave and the superconducting instabilities cancel each other and th ere is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.