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Open AccessJournal ArticleDOI

The Hubbard Model

- 10 Mar 2022 - 
- Vol. 13, Iss: 1, pp 239-274
TLDR
The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field as discussed by the authors . Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials.
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 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.

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The Hubbard Model: A Computational Perspective

TL;DR: 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 as mentioned in this paper .
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Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

TL;DR: The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman, and concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential ''killer application'' as mentioned in this paper .
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Engineering topological states in atom-based semiconductor quantum dots

TL;DR: In this article , the authors show that for precision-placed atoms in silicon with strong Coulomb confinement, they can engineer a minimum of six all-epitaxial in-plane gates to tune the energy levels across a linear array of ten quantum dots to realize both the trivial and the topological phases of the many-body Su-Schrieffer-Heeger (SSH) model.
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Extended Bose–Hubbard model with dipolar excitons

TL;DR: In this paper , the authors show that dipolar excitons enable controlled implementations of boson-like arrays with strong off-site interactions, in lattices with programmable geometries and more than 100 sites.
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Magnetic correlations in infinite-layer nickelates: An experimental and theoretical multimethod study

TL;DR: In this article , a comprehensive study of magnetic correlations in LaNiO$(2) , a parent compound of the recently discovered family of infinite-layer (IL) nickelate superconductors, using multiple experimental and theoretical methods is presented.
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