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Jordan-Wigner transformation provides an exact solution for transverse field Ising model in both the ferromagnetic phase and the paramagnetic phase. Yet this seems to imply that in both phases, the elementary excitation is fermion. This is counterintuitive since in the paramagnetic phase, the elementary excitation is a single spin flip, which carries spin-1 and therefore should be regarded boson like a conventional magnon. How to reconcile this?

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