Ground state properties of antiferromagnetic Heisenberg spin rings

TL;DR

This paper investigates the exact ground state properties of antiferromagnetic Heisenberg spin rings with various configurations, revealing systematic behaviors and conjecturing general properties applicable to all such rings.

Contribution

It provides a comprehensive analysis of ground states in antiferromagnetic Heisenberg spin rings using exact diagonalization, extending understanding beyond bipartite lattices.

Findings

Ground state degeneracy relates to number of spins and quantum numbers.

Numerical results align with rigorous proofs in certain cases.

Conjecture that properties hold for all antiferromagnetic Heisenberg spin rings.

Abstract

Exact ground state properties of antiferromagnetic Heisenberg spin rings with isotropic next neighbour interaction are presented for various numbers of spin sites and spin quantum numbers. Earlier work by Peierls, Marshall, Lieb, 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 behaviour 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.