The Hubbard Model

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 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.

Automated summary

The repulsive Hubbard model is crucial for understanding strongly correlated electron systems and exhibits rich phenomenology. However, its phase diagram is still controversial. In this review, we summarize the known information about the model and focus on the ground state properties and important unresolved questions.