Jordan–Wigner transformation
Mathematical mapping in quantum mechanics / From Wikipedia, the free encyclopedia
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The Jordan–Wigner transformation is a transformation that maps spin operators onto fermionic creation and annihilation operators. It was proposed by Pascual Jordan and Eugene Wigner[1] for one-dimensional lattice models, but now two-dimensional analogues of the transformation have also been created. The Jordan–Wigner transformation is often used to exactly solve 1D spin-chains such as the Ising and XY models by transforming the spin operators to fermionic operators and then diagonalizing in the fermionic basis.
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This transformation actually shows that the distinction between spin-1/2 particles and fermions is nonexistent. It can be applied to systems with an arbitrary dimension.