Heisenberg Hamiltonian

1. Oct 20, 2005

somy

Hi.
Can anyone tell me what exactly the "Heisenberg Hamiltonian" is???
I found it in an article related to: the renormalization group.
Somy

2. Oct 21, 2005

dextercioby

I haven't seen such thing either. Why don't you quote the paragraph from the article? The context should make sense, i suppose.

Daniel.

3. Oct 21, 2005

inha

The Heisenberg Hamiltonian I'm aware of is related to magnetism. It's the exchange energy between the spins
$$H=\sum_i \sum_{j \ne i} J_{ij} S_i \cdot S_j$$

4. Oct 24, 2005

elhinnaw

I could be wrong about this since it is venturing out of my area of knowledge, but isn't the Heisenberg Hamiltonian just the regular Hamiltonian in the reference frame of the Hamiltonian operator?

If I am wrong, what exactly the Heisenberg picture of operators?

5. Oct 25, 2005

snooper007

Inha iscorrect, Heisenberg picture of operators means that
$$O_H=e^{-iHt}O_Se^{iHt}$$
$$O_H, O_S$$ are operators in Heisenberg and Schroedinger pictures.

6. Oct 29, 2005

somy

but I thout it was related to solid state of matter. the hamiltonian of the linking energies.
yes???

7. Oct 29, 2005

inha

Yes. That's what I posted, magnetism is a property of solids too.