Physics

Phenomenology (philosophy)

Statistical physics

Hubbard model

Epistemology

Philosophy

Simplicity

Theoretical physics

Phase (matter)

Superconductivity

Quantum mechanics

Ground state

Quantum

Phase diagram

Annual Review of Condensed Matter Physics

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.

The Hubbard Model