Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

Details Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

2003-03-19

arxiv.org/abs/cond-mat/0303386v1

Phys. Rev. B 68 (2003) 054422

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevB.68.054422

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.

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