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RKKY interraction

  1. Oct 23, 2012 #1
    Hamiltonian of interaction between fixed ion and conducting electron
    ##\hat{H}=-J\sum_{i=1}^2\{\hat{s}_i^z\hat{S}_i^z+\frac{1}{2}(\hat{s}_i^+\hat{S}_i^{-}+\hat{s}_i^-\hat{S}_i^{+})\}##
    Why both electron and ion are defined with subscript ##i##?
     
  2. jcsd
  3. Oct 26, 2012 #2
    ...and why does i run from 1 to 2?

    Looks like a bug to me.

    One would think that you need seperate indices i and j to label the atoms and the (conduction) electrons, and that these would run over the number of particles in question.
     
  4. Oct 26, 2012 #3
    There is two fixed ions. One ion polarised electron and that electron interract with secound ion. So between ions is indirect interraction.
     
  5. Oct 26, 2012 #4
    OK, that makes sense. However, I would still expect the electron index to be independent of the ion. Remember that RKKY occurs in the conduction electrons of metals.
     
  6. Oct 26, 2012 #5
    Well I think that if electron is near ion you could approximate that it is on the same lattice site ion lattice site. I asked question about calculating matrix element in this problem.
    Here is that question.
    https://www.physicsforums.com/showthread.php?t=646675

    I would be grateful if you could look and maybe answer this question.
     
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