Luttinger Liquid in a Solvable 2-Dimensional Model

TL;DR

This paper introduces a solvable 2D model of spinless electrons with a specific spectrum, demonstrating non-Fermi liquid behavior and Luttinger liquid characteristics through bosonization, with no symmetry breaking.

Contribution

It presents a 2D electron model exhibiting Luttinger liquid behavior, solved exactly via bosonization, and shows the cancellation of density wave and superconducting instabilities.

Findings

Breakdown of Landau Fermi liquid indicated by electron lifetime calculation

No symmetry breaking due to cancellation of instabilities

Excitation spectrum consists of gapless bosonic modes similar to 1D Luttinger liquids

Abstract

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