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After considering the thread
https://www.physicsforums.com/showthread.php?t=474384
I began to think about the bonding in graphene.
As long as we can neglect electron electron interaction, the ground state can be obtained almost trivially in a tight binding approximation. On the other hand, chemists tend to think of graphene in terms of valence bond structures. In the case of graphene where electron electron interaction is weak, this would mean to consider resonance structures with a high percentage of ionic bonds. But when one considers the Hubbard model in the high U limit (which does not correspond to the situation in graphene), I would guess a valence bond ground state with no ionic structures. There are only three distinct ones which are of "quinonic" character, and which have no overlapp in the infinite lattice limit.
So I would expect a symmetry breaking with three degenerate ground states.
On the other hand in the article cited below, I found the statement that there exists a theorem which shows that the ground state of the Hubbard model is unique at half filling. How does this fit together?
http://www.google.de/url?sa=t&sourc...sg=AFQjCNH49hDGlw8bPhAr-LSKnJK7hPoAWQ&cad=rja
Edit: Well, now that I think about it, the structures that I had in mind are not the only ones (although I had them seen somewhere in my chemistry book long ago). Also, the high U limit of the Hubbard model should reduce to the Heisenberg model. So it seems that actually I am interested in the resonating valence bond ground state of the Heisenberg model.
https://www.physicsforums.com/showthread.php?t=474384
I began to think about the bonding in graphene.
As long as we can neglect electron electron interaction, the ground state can be obtained almost trivially in a tight binding approximation. On the other hand, chemists tend to think of graphene in terms of valence bond structures. In the case of graphene where electron electron interaction is weak, this would mean to consider resonance structures with a high percentage of ionic bonds. But when one considers the Hubbard model in the high U limit (which does not correspond to the situation in graphene), I would guess a valence bond ground state with no ionic structures. There are only three distinct ones which are of "quinonic" character, and which have no overlapp in the infinite lattice limit.
So I would expect a symmetry breaking with three degenerate ground states.
On the other hand in the article cited below, I found the statement that there exists a theorem which shows that the ground state of the Hubbard model is unique at half filling. How does this fit together?
http://www.google.de/url?sa=t&sourc...sg=AFQjCNH49hDGlw8bPhAr-LSKnJK7hPoAWQ&cad=rja
Edit: Well, now that I think about it, the structures that I had in mind are not the only ones (although I had them seen somewhere in my chemistry book long ago). Also, the high U limit of the Hubbard model should reduce to the Heisenberg model. So it seems that actually I am interested in the resonating valence bond ground state of the Heisenberg model.
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