Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

Abstract

We suggest a general rule for the shift quantum numbers k of the relative ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even rings. Our rule is confirmed by numerical investigations and rigorous proofs for special cases, including systems with a Haldane gap. Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model.

8 pages, 2 figures, submitted to Phys. Rev. B. More information at http://www.physik.uni-osnabrueck.de/makrosysteme/