Difference between Hubbard and Heisenberg-model

[Abigale]

Hi,
I read a chapter about the Heisenberg-model,
and then something about the Hubbard-Model.
The Heisenberg-model just shows, that neighbouring spins allign antiparallel if J<0.
The Hubbard-Model says, that there is a hopping probability t and an Coulomb replsion,
so that a material becomes metal or insulator.

I read that for the Hubbard-Model J=2t^2/U, where does this come from?

Thank you

 

[DrDu]

The Heisenberg model can be viewed at as the large U limit of the Hubbard model. The states of lowest energy are those with the least number of double occupied sites. For these states, you can do a perturbation expansion in 1/U to get J.