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We investigate the application of matrix product states to the Hubbard modelin one spatial dimension with both of open and periodic boundary conditions. Wedevelop the variatinal method that the optimization of the variationalparameters is carried out locally and sequentially in the framework of matrixproduct operators (MPO) by including the sign, due to the anti-commutationrelation of fermion operators, in the matrix element of MPO. The numericalaccuracy of the ground state energy is examined.

Application of matrix product states to the Hubbard model in one spatial dimension