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This question is relevant to the one enter link description here

As one answered in that question, different fermions species also follow anti-commutation.

But why in transverse Ising field, spins on differents sites commute while on the same site anti-commute? At first I thought it's because distinguishability.

But the answer in that question clearly hints distinguishability is not the reason for anti-commutation, because different fermion species are obviously distinguishable.

So could any one help to explain why in transverse Ising field, spins on differents sites commute while on the same site anti-commute?

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    $\begingroup$ Klein transformation comes into my mind $\endgroup$
    – Tobias Fünke
    Commented Apr 18 at 10:00
  • $\begingroup$ So it's just a redifition without deep physics behind it? $\endgroup$
    – xiang sun
    Commented Apr 21 at 9:15

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