The Hubbard model: basic notions and selected applications

TL;DR

This paper provides a comprehensive introduction to the Hubbard model, covering its fundamental concepts, calculation methods, and applications to one- and two-dimensional systems, integrating both original and literature-based results.

Contribution

It offers a self-contained overview of the Hubbard model's basic notions and demonstrates its applications to low-dimensional systems with combined original and existing findings.

Findings

Application of the Hubbard model to 1D and 2D systems

Discussion of calculation methods within the model

Integration of author's results with literature

Abstract

The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the motivation for its development to the formulation of the Hamiltonian,and some methods of calculation within the model. The second part will discuss some applications of the model to 1D and 2D systems,based on a combination of the author's results with those from the literature.