The Hubbard Model

TL;DR

This paper reviews the Hubbard model, a fundamental framework for understanding strongly correlated electrons, focusing on its ground state properties in two dimensions and highlighting unresolved questions.

Contribution

It synthesizes known exact and approximate results for the Hubbard model's ground states, emphasizing two-dimensional systems and discussing open research questions.

Findings

Ground state properties vary across different lattice geometries.

Controlled solutions provide insights into phase behavior.

Many open questions remain in understanding the model fully.

Abstract

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions.