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The Hubbard Model
- Daniel P. Arovas1, Erez Berg2, Steven A. Kivelson3, and Srinivas Raghu3,4
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View Affiliations Hide AffiliationsAffiliations: 1Department of Physics, University of California, San Diego, La Jolla, California, USA 2Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 3Department of Physics, Stanford University, Stanford, California, USA; email: [email protected] 4Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California, USA
- Vol. 13:239-274 (Volume publication date March 2022) https://doi.org/10.1146/annurev-conmatphys-031620-102024
- First published as a Review in Advance on November 18, 2021
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Copyright © 2022 by Annual Reviews. All rights reserved
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.
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