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Luttinger Liquid in a Solvable 2-Dimensional Model

R. Hlubina
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Abstract

We consider spinless electrons in two dimensions with the bare spectrum $ε({\bf p})=|p_x|+|p_y|$. 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.

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R. Hlubina. 1993-12-21. Luttinger Liquid in a Solvable 2-Dimensional Model. https://doi.org/10.1103/physrevb.50.8252

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