The Hubbard Model
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. read more
Citations
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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
Seunghoo Lee,Joonho Lee,Huanchen Zhai,Yu Tong,Alexander M. Dalzell,Ashutosh Kumar,Phillip Helms,Johnnie Gray,Zhiqiang Cui,Wenyuan Liu,Michael J. Kastoryano,Ryan Babbush,John Preskill,David R. Reichman,E. M. Campbell,Edward F. Valeev,Lin Lin,Garnet Kin-Lic Chan +17 more
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
M. Kiczynski,S. K. Gorman,Haiyu Geng,Matthew Donnelly,Yen-Tung Chung,Y. He,J. G. Keizer,Michelle Y. Simmons +7 more
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
Camille Lagoin,Utso Bhattacharya,Tobias Graß,Ravindra W. Chhajlany,Tymoteusz Salamon,Kirk W. Baldwin,L. N. Pfeiffer,Maciej Lewenstein,Markus Holzmann,F. Dubin +9 more
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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