Luttinger Liquid in a Solvable 2-Dimensional Model

Abstract

We consider spinless electrons in two dimensions with the bare spectrum $\epsilon (\mathbf{p})=|p_x|+|p_y|$. 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 the Landau Fermi liquid 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.

13 pages, 1 figure upon request, REVTEX, ETH-TH/93-50

References in corpus (1)

• Bosonization and Fermion Liquids in Dimensions Greater Than One

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• Gauge invariance, correlated fermions, and photon mass in 2+1 dimensions