A 2D Luttinger model

TL;DR

This paper derives a 2D low-energy effective model for spinless fermions on a square lattice, enabling exact bosonization and providing insights into the lattice system's physical properties.

Contribution

It presents a novel derivation of a 2D effective model using a justified continuum limit, facilitating bosonization analysis of lattice fermions.

Findings

Effective 2D model derived for spinless fermions

Model can be treated with exact bosonization methods

Provides a framework to analyze lattice fermion systems

Abstract

A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is shown that the effective model thus obtained can be treated by exact bosonization methods. It is also discussed how this effective model can be used to obtain physical information about the corresponding lattice fermion system.