1 D lattice

  1. I have a question if you have an Hamiltonian given by
    [itex]
    H = \sum_{i,i+1} \sigma_i \cdot \sigma_{i+1}
    [/itex]
    where i can even or odd bonds so in a 1D lattice so if you have 4 sites(1 2 3 4 1) then (12) and (34) are even bonds and (23) and (41) are odd bonds. and I was checking if

    [itex]
    [H_{x even(12)} , H_{x even(34)}]
    [/itex]
    will they commute also do even and odd bonds commute i.e.
    [itex]
    [H_{x even} , H_{x odd}]
    [/itex]
     
  2. jcsd
  3. DrDu

    DrDu 4,452
    Science Advisor

    How do you define ##H_{xeven}## and ##H_{xodd}##?
     
  4. Same as I defined above its a Heisenberg spin systems with
    [tex]
    H_{xeven}
    [/itex] and
    [tex]
    H_{xodd}
    [/itex]

    are both Heisenberg spin systems with spins defined for even and odd bonds. Here when I say bond I mean the distance between two atomic points in lattice. and alternative bonds are defined as even and odd. Also my ultimate goal is to calculate
    [tex]
    [ (\sigma_{1}^x \cdot \sigma_{2}^x + \sigma_{1}^y \cdot \sigma_{2}^y + \sigma_{1}^z \cdot \sigma_{2}^z) , (\sigma_{3}^x \cdot \sigma_{4}^x + \sigma_{3}^y \cdot \sigma_{4}^y + \sigma_{3}^z \cdot \sigma_{4}^z)]
    [/itex]
    so will it commute.
     
    Last edited: Jan 28, 2014
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