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Level degeneracy of the transverse ising model

  1. Jul 29, 2011 #1
    the hamiltonian is

    H=-J \sum_{l=1}^N \sigma_l^z \sigma_{l+1}^z+ g \sigma_l^x

    here we assume periodic boundary condition

    my problem is, what is the highest possible degeneracy of the levels?

    initially i expected 2

    but numerically i find that it is 4

    i cannot understand it
  2. jcsd
  3. Jul 29, 2011 #2
    it is not even 4

    it can be higher

    i just noticed that since the single particle excitation spectrum is symmetric, the multiple excitation spectrum can be highly degenerate

    but i cannot see the symmetry behind
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