I have a question if you have an Hamiltonian given by(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

H = \sum_{i,i+1} \sigma_i \cdot \sigma_{i+1}

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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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# 1 D lattice

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