Difference between Hubbard and Heisenberg-model

In summary, the Heisenberg model is a simplified version of the Hubbard model, where neighboring spins align in opposite directions if J<0. The Hubbard model, on the other hand, involves a hopping probability and Coulomb repulsion, determining whether a material becomes a metal or insulator. The formula J=2t^2/U for the Hubbard model comes from a perturbation expansion in 1/U to find the states of lowest energy.
  • #1
Abigale
56
0
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
 
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  • #2
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.
 

What is the difference between the Hubbard and Heisenberg models?

The Hubbard and Heisenberg models are two different mathematical models used to describe the behavior of particles in a system. The main difference between these models lies in the type of particles they consider and the interactions between them.

Which particles are considered in the Hubbard and Heisenberg models?

The Hubbard model considers electrons as the particles in a system, while the Heisenberg model considers magnetic moments, such as electron spins, as the particles.

How do the interactions between particles differ in the Hubbard and Heisenberg models?

In the Hubbard model, the electrons interact through Coulombic forces, while in the Heisenberg model, the magnetic moments interact through exchange interactions.

What are the applications of the Hubbard and Heisenberg models?

The Hubbard model is commonly used in condensed matter physics to study the behavior of electrons in solids, while the Heisenberg model is often used in studying magnetic materials and their properties.

Can the Hubbard and Heisenberg models be combined?

Yes, the two models can be combined to form the Hubbard-Heisenberg model, which allows for the study of both electron and magnetic interactions in a system. This model is often used in investigating complex materials that exhibit both electronic and magnetic properties.

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