LUTTINGER LIQUID IN A SOLVABLE 2-DIMENSIONAL MODEL

We consider spinless electrons in two dimensions with the bare spectrum epsilon(p) = v(F)(\p(z)\ + \p(y)\). In momentum space, the interactions among electrons have a finite range q(0), which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indicates a breakdown of Landau's Fermi-Liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there 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.