Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

TL;DR

This paper proposes a general rule for determining the shift quantum numbers of the relative ground states in antiferromagnetic Heisenberg spin rings, extending previous results and confirmed by numerical and rigorous methods.

Contribution

It introduces a new, generalized rule for shift quantum numbers applicable to a broad class of antiferromagnetic spin rings, including systems with a Haldane gap.

Findings

The rule is confirmed by numerical investigations.

Rigorous proofs support the rule for special cases.

Implications for total spin quantum number S are discussed.

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.