# 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.
Thanks in advance.
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.

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