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Expanding the Hamiltonian around a point of symmetry

  1. Feb 27, 2015 #1
    Hey
    I have a tight binding Hamiltonian of a BCC lattice which is a 4x4 matrix in k space (the 4 elements correspond to 4 atoms that are in a unit cell)
    I want to expand it for small k's around the symmetry points P or Gamma or H.
    I'm looking at a paper by J. L. Ma˜nes, PHYSICAL REVIEW B 85, 155118 (2012), where he is doing this by some kind of Unitary transformation to the Hamiltonian that changes the basis from the four Bloch functions basis to the "symmetry-adapted basis". I didn't find an explanation in the paper to the operator he uses to go from one basis to another, and i don't understand what is this symmetry adapted basis anyway.
    If anyone understand this i would be very happy to know :)


    http://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.155118
     
  2. jcsd
  3. Feb 27, 2015 #2

    DrDu

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  4. Feb 27, 2015 #3
    hey DrDu
    since i dont have a very good background on group theory (abstract math is not my strong suit.. \:), and since it looks like a more general subject, is there a more concentrated example that applies this method strictly to the problem at hand? (i.e changing the basis of a tight binding Hamiltonian)

    Thanks!
     
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