Ground-state and low-lying excitations of the periodic Anderson Hamiltonian in one dimension from finite-cell calculations

We present the calculations of the ground state and lowest excited states of the one-dimensional periodic Anderson Hamiltonian with two electrons per site and arbitrary magnitude of the repulsive interaction $U$. We consider finite cells (up to $N=4\mathrm{}$) and introduce a new method, using modified periodic boundary conditions, to facilitate comparison of calculations with different $N$. The ground state is found to be a nonmagnetic singlet in all cases. The lowest-energy excitations for adding or subtracting one 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 one dimension. The lowest excitations are shown to vary little with $N$ and, for $N=4\mathrm{}$, the results agree well with infinite-cell calculations, both for small $U$ and for the Kondo-lattice regime. The primary results are the continuous variation from $U=0\mathrm{}$ to the Kondo-lattice and mixed-valence regimes and the importance of correlations, which lead to the insulating gap and dispersion in the electronic and spin excitations.