Fermions in two dimensions, bosonization, and exactly solvable models

TL;DR

This paper explores exactly solvable two-dimensional fermion models using bosonization, reviewing recent developments and solutions, with implications for lattice systems and high-temperature superconductivity.

Contribution

It presents new insights into the relation between Mattis' model and lattice fermion systems, including exact solutions and extensions of the model.

Findings

Established a connection between a variant of Mattis' model and lattice fermions

Provided exact solutions for the models discussed

Discussed implications for high-Tc superconductivity

Abstract

We discuss interacting fermion models in two dimensions, and, in particular, such that can be solved exactly by bosonization. One solvable model of this kind was proposed by Mattis as an effective description of fermions on a square lattice. We review recent work on a specific relation between a variant of Mattis' model and such a lattice fermion system, as well as the exact solution of this model. The background for this work includes well-established results for one-dimensional systems and the high-Tc problem. We also mention exactly solvable extensions of Mattis' model.