1 D lattice


by adityaphysics
Tags: heisenberg, lattice
adityaphysics
adityaphysics is offline
#1
Jan27-14, 06:11 PM
P: 2
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]
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DrDu
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#2
Jan28-14, 12:53 AM
Sci Advisor
P: 3,370
How do you define ##H_{xeven}## and ##H_{xodd}##?
adityaphysics
adityaphysics is offline
#3
Jan28-14, 02:30 AM
P: 2
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.


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