Properties of the periodic Anderson Hamiltonian: Calculations on finite cells

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Abstract
We present calculations for the ground state and the lowest excited states of the one-dimensional periodic Anderson Hamiltonian with two electrons per site and arbitrary magnitude of the repulsion parameter U. We present exact numerical results for finite cells (up to N = 4) and introduce ’’modified’’ periodic boundary conditions to facilitate the extrapolation for larger N. The lowest energy excitations for adding or subtracting an electron show that the system is insulating, and the lowest spin-flip excitations indicate a near instability to antiferromagnetism due to the ’’nesting’’ of the Fermi surface in 1d. For N = 4 the results agree well with infinite cell calculations both for small U and for large U in the Kondo lattice limit. The primary results are the continuous variation from the U = 0 to the Kondo lattice and mixed valence regimes and the importance of correlations, omitted in the impurity calculations, which lead to an insulating gap and dispersion in the electronic and magnetic excitations.