Application of the Schur–Weyl Duality in the One-Dimensional Hubbard Model

We present an application of the Schur–Weyl duality in the one-dimensional Hubbard model in the case of a half-filled system of any number of atoms. We replace the actions of the dual symmetric and unitary groups in the whole 4N-dimensional Hilbert space by the actions of the dual groups in the spin and pseudo-spin spaces. The calculations significantly reduce the dimension of the eigenproblem of the one-dimensional Hubbard model.