Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

Klaus Bärwinkel; Peter Hage; Heinz-Jürgen Schmidt; Jürgen Schnack

doi:10.1103/PhysRevB.68.054422

Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

Klaus Bärwinkel, Peter Hage, Heinz-Jürgen Schmidt, and Jürgen Schnack

Phys. Rev. B 68, 054422 – Published 26 August 2003

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 the 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 for $\vec{N} \infty .$ Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model.

Received 24 March 2003

DOI:https://doi.org/10.1103/PhysRevB.68.054422

Authors & Affiliations

Klaus Bärwinkel^*, Peter Hage^†, Heinz-Jürgen Schmidt^‡, and Jürgen Schnack^§

Universität Osnabrück, Fachbereich Physik, D-49069 Osnabrück, Germany

^*Electronic address: Klaus.Baerwinkel@uos.de
^†Electronic address: phage@uos.de
^‡Electronic address: hschmidt @uos.de
^§Electronic address: jschnack@uos.de

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Vol. 68, Iss. 5 — 1 August 2003

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