Abstract
Exact ground-state properties of antiferromagnetic Heisenberg spin rings with isotropic next-neighbor interaction are presented for various numbers of spin sites and spin quantum numbers. Earlier work by Peierls, Marshall, Leib, Schultz and Mattis focused on bipartite lattices and is not applicable to rings with an odd number of spins. With the help of exact diagonalization methods we find a more general systematic behavior which for instance relates the number of spin sites and the individual spin quantum numbers to the degeneracy of the ground state. These numerical findings all comply with rigorous proofs in the cases where a general analysis could be carried out. Therefore, it can be plausibly conjectured that the ascertained properties hold for ground states of arbitrary antiferromagnetic Heisenberg spin rings.
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