Exact Eigenstates of the Hubbard Model Independent of the On‐Site Electron Interaction

Exact Eigenstates of the Hubbard Model Independent of the On‐Site Electron Interaction IntroductionThe Hubbard model for electrons was proposed in 1963, and now is used widely to understand the theoretical mechanism of the high temperature superconductivity. In the Hubbard model, except for single‐electron hopping terms, there are also on‐site interactions for electrons occupying the same lattice site in coordinate space. It is difficult to solve the Hubbard model except in one dimension. In 1990, Yang and Zhang found that the model had a SO4 symmetry and constructed many exact eigenstates that were independent of the on‐site electron interaction strength U. They believed that they had found all the U‐independent eigenstates of the model, but they did not know how to prove the statement. In this paper we show that their statement is incorrect by giving many new U‐independent exact eigenstates of the model. Our results are demonstrated in two‐dimensional Hubbard model, but many results can be easily extended to higher dimensions.The Hubbard model for electrons on a periodic two‐dimensional L×L lattice, where L is even, is defined by the HamiltonianH=H0+Hint,H0=−t∑〈r,r′〉(ar†ar′+br†br′+H.c.),Hint=U∑rar†arbr†br,where 〈r,r′〉 means the sum is over the nearest‐neighbor pairs, ar and br are annihilation operators for spin‐up and spin‐down electrons in coordinate space, respectively, and r = (x,y) designates the L×L lattice sites http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physica Status Solidi (B) Basic Solid State Physics Wiley

Exact Eigenstates of the Hubbard Model Independent of the On‐Site Electron Interaction

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISSN
0370-1972
eISSN
1521-3951
D.O.I.
10.1002/pssb.201700321
Publisher site
See Article on Publisher Site

Abstract

IntroductionThe Hubbard model for electrons was proposed in 1963, and now is used widely to understand the theoretical mechanism of the high temperature superconductivity. In the Hubbard model, except for single‐electron hopping terms, there are also on‐site interactions for electrons occupying the same lattice site in coordinate space. It is difficult to solve the Hubbard model except in one dimension. In 1990, Yang and Zhang found that the model had a SO4 symmetry and constructed many exact eigenstates that were independent of the on‐site electron interaction strength U. They believed that they had found all the U‐independent eigenstates of the model, but they did not know how to prove the statement. In this paper we show that their statement is incorrect by giving many new U‐independent exact eigenstates of the model. Our results are demonstrated in two‐dimensional Hubbard model, but many results can be easily extended to higher dimensions.The Hubbard model for electrons on a periodic two‐dimensional L×L lattice, where L is even, is defined by the HamiltonianH=H0+Hint,H0=−t∑〈r,r′〉(ar†ar′+br†br′+H.c.),Hint=U∑rar†arbr†br,where 〈r,r′〉 means the sum is over the nearest‐neighbor pairs, ar and br are annihilation operators for spin‐up and spin‐down electrons in coordinate space, respectively, and r = (x,y) designates the L×L lattice sites

Journal

Physica Status Solidi (B) Basic Solid State PhysicsWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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