The Hubbard model: A computational perspective

TL;DR

This paper reviews the Hubbard model, highlighting its significance in understanding correlated electron systems, recent advances in numerical methods, and the diverse phenomena it exhibits, emphasizing progress in computational approaches.

Contribution

It provides an overview of the Hubbard model, discusses key questions, and illustrates recent computational progress in revealing its complex correlation physics.

Findings

Numerical methods have achieved quantitative accuracy in studying the model.

The model exhibits a rich variety of phases and correlation phenomena.

Recent computational advances have deepened understanding of the model's physics.

Abstract

The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. While analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impressive progress in achieving quantitative accurate results over the last years. This article gives an introduction to the model, motivates common questions, and illustrates the progress that has been achieved over the last years in revealing various aspects of the correlation physics of the model.