We present the application of the Schur-Weyl duality in the one-dimensional Hubbard model in the case of half-filled system of any numer of atoms. We replace the actions of the dual symmetric and unitary groups in the whole 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.

中文翻译：

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Schur-Weyl对偶在一维哈伯德模型中的应用

我们展示了 Schur-Weyl 对偶性在一维 Hubbard 模型中的应用，适用于任意数量原子的半填充系统。我们用自旋和伪自旋空间中对偶群的作用代替了整个希尔伯特空间中对偶对称和酉群的作用。计算显着降低了一维哈伯德模型的特征问题的维数。