The Hubbard Model

Daniel P Arovas; Erez Berg; Steven A Kivelson; Srinivas Raghu

doi:10.1146/annurev-conmatphys-031620-102024

The Hubbard Model

Daniel P Arovas, Erez Berg, Steven A Kivelson, Srinivas Raghu

Department of Condensed Matter Physics

Research output: Contribution to journal › Review article › peer-review

302 Citations (Scopus)

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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 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.

Original language	English
Pages (from-to)	239-274
Number of pages	36
Journal	Annual Review of Condensed Matter Physics
Volume	13
DOIs	https://doi.org/10.1146/annurev-conmatphys-031620-102024
Publication status	Published - 2022

Funding

It is a pleasure to acknowledge numerous extremely helpful discussions about the Hubbard model and related topics with too many colleagues to list. In particular, however, the writing of this paper was greatly assisted by input from Ian Affleck, Assa Auerbach, Vladimir Calvera, Andrey Chubukov, Youjin Deng, Tom Devereaux, Eduardo Fradkin, Zhaoyu Han, HongChen Jiang, Elliott Lieb, Dror Orgad, Mohit Randeria, Doug Scalapino, and Richard Scalettar. S.A.K. was supported, in part, by the National Science Foundation (NSF) under grant number DMR2000987. E.B. acknowledges support from the European Research Council (ERC) under grant HQMAT (grant agreement number 817799). S.R. was supported in part by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515.

All Science Journal Classification (ASJC) codes

General Materials Science
Condensed Matter Physics

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10.1146/annurev-conmatphys-031620-102024

eb_AnnualRevCondensedMatterPhy_TheHubbardModel_AM2021.pdfAccepted author manuscript, 990 KBLicence: Other

https://arxiv.org/abs/2103.12097Licence: CC BY

Cite this

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AB - 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.

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DO - 10.1146/annurev-conmatphys-031620-102024

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EP - 274

JO - Annual Review of Condensed Matter Physics

JF - Annual Review of Condensed Matter Physics

ER -

The Hubbard Model

Abstract

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