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-   -   COMPLETE Derivation of Heisenberg and Hubbard Models? (http://www.physicsforums.com/showthread.php?t=585200)

maverick_starstrider Mar8-12 10:53 PM

COMPLETE Derivation of Heisenberg and Hubbard Models?
 
Does anyone know of a COMPLETE derivation of the Hubbard Model and then the Heisenberg model from it. What I mean by complete is pedagogical including all (or at least most) steps. Books like Assa Auerbach's and Altland and Simons are worthless for these kind of things (in fact IMHO those books are worthless to learn ANYTHING from), they generally pull out some somewhat arcane perturbation technique and transformation and matrix relation out of the ether and then skip all steps and write down the "answer". This seems to be par for the course in all expositions I've found. Furthermore every "derivation" I've seen is only for a two state system and ends with the claim that generalizing to N-states is "trivial", anyone know of a place where someone degrades themselves so much to actually attempt this generalization in a textbook or lecture note? I suppose it's a pipe dream but the key questions I'd like to find a source to answer is stuff like:

-What is this esoteric perturbation theory involving projectors, is it equivalent to standard perturbation theory? (If so why bother with it?)
-What is the complete expansion? What are the higher order terms (isn't this where ring exchange comes from)? Why are they discarded?
-How does the derivation change if it's not spin 1/2?

I know it's generally the attitude of most condensed matter books for authors not to stoop so low as to provide such trifling details but is there maybe some lecture notes somewhere or the likes that derives these things?


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