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Derivation of the Hamiltonian of the Heisenberg model

  1. Oct 21, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that the Hamiltonian of the Heisenberg model can be written as:
    [tex]H=\sum^{N}_{k=1}[H_{z}(k)+H_{f}(k)][/tex]
    where
    [tex]H_{z}(k)\equivS^{z}(k)S^{z}(k+1)[/tex]
    [tex]H_{f}(k)\equiv(1/2)[S^{+}(k)S^{-}(k+1)+S^{-}(k)S^{+}(k+1)][/tex]

    2. Relevant equations
    As above


    3. The attempt at a solution
    I read through this page: http://phycomp.technion.ac.il/~riki/H2_molecule.html
    but I still don't really understand.
     
  2. jcsd
  3. Oct 21, 2007 #2
    Sorry that second equation should be
    Hz(k)=S^z(k)S^z(k+1)
     
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