The Hubbard Model: Some Rigorous Results and Open Problems

TL;DR

This paper reviews rigorous results and open problems related to the Hubbard model, a fundamental yet complex model of interacting electrons that shares features with the Ising model but remains analytically challenging.

Contribution

It summarizes what is known rigorously about the Hubbard model and highlights open problems that could be addressed through mathematical analysis.

Findings

Summary of rigorous results on the Hubbard model

Identification of key open problems in the field

Discussion of the model's complexity compared to the Ising model

Abstract

Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many ``real world'' features, but it is much more difficult to analyze qualitatively than the Ising model. After a third of a century of research, we are still not sure about many of its basic properties. This mini-review will explore what is known rigorously about the model and it will attempt to describe some open problems that are possibly within the range of rigorous mathematical analysis.