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: ; ; ;
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.
All for just $49/month
Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.
Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.
It’s easy to organize your research with our built-in tools.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera