A two dimensional analogue of the Luttinger model

TL;DR

This paper introduces a 2D fermion model as an analogue to the Luttinger model, derived from a lattice system, with exact bosonization and mean field approaches to analyze its properties.

Contribution

It proposes a novel 2D Luttinger-like fermion model derived from lattice systems, with exact bosonization and mean field methods for analysis.

Findings

Model derived as a continuum limit of 2D lattice fermions

Exact bosonization of parts of the model

Proposed mean field treatment for remaining degrees of freedom

Abstract

We present a fermion model that is, as we suggest, a natural 2D analogue of the Luttinger model. We derive this model as a partial continuum limit of a 2D spinless lattice fermion system with local interactions and away from half filling. In this derivation, we use certain approximations that we motivate by physical arguments. We also present mathematical results that allow an exact treatment of parts of the degrees of freedom of this model by bosonization, and we propose to treat the remaining degrees of freedom by mean field theory.