Study Of Spin Fermionization

In the thesis we firstly introduce one-dimensional spin 1/2 Jordan-Wigner transformation.Then the application that one-dimensional spin 1/2 Jordan-Wigner transformation is used for one spin chain model is displayed and one-dimensional spin 3/2 Jordan-Wigner transformation is discussed.From one-dimensional totwo-dimensional, we discuss two-dimensional spin 1/2 Jordan-Wigner transformation. At last,two models in which two-dimensional spin 1/2 Jordan-Wigner transformation have been applied are presented.Chapter 1: Firstly, one-dimensional spin 1/2 Jordan-Wigner transformation thatmaps the spin operators into fermions is introduced, which maps spin model into spinsless fermions model.Next,we discuss the statistical relations of spin operators by means of this mapping. Then the application that one-dimensionalspin 1/2 Jordan-Wigner transformation is used for one-dimensional anisotropic XY model is displayed.Chapter2: New Jordan-Wigner-type transformation between spin 3/2 and fermionsof two type is shown. By using the double-fermion representation,we discuss thestatistical relations of the s = 3/2 spin operator.Chapter3: Based upon one-dimensional transformation, We discuss the estensions for two dimensions suggested by M.Azzouz and Y.R.Wang.Chapter4: The application that two-dimensional spin 1/2 Jordan-Wignertransformation are used for two spin chain models are displayed.Firstly,the mean-field-like treatment of the Jordan-Wigner fermions for the isotropic XY model is discussed in detail.Then the consideration of Heisenberg model with Ising term in fermionic language is given separately.