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
Physica Status Solidi (B) Basic Solid State Physics – Wiley
Published: Jan 1, 2018
Keywords: ; ; ;
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