Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect

Abstract

The sequence of $2s+1$ ground states in the frustrated antiferromagnetic rings with odd number $n$ of local spins $s$ resulting from a single bond defect strength is determined, and occurrence of the Lieb-Mattis energy level ordering, proven for the bipartite systems only, is confirmed for the rings in question. The sequence is universal, provides the theoretical basis for the recent classification of spin frustration in molecular magnets, and indicates that the Lieb-Mattis theorem (LMT) consequences exist for the nonbipartite rings. The states in the sequence are characterized by the total spin $S$ fulfilling the constraint $S\ensuremath{\le}s$ and are separated by $2s$ Kahn degenerate frustration points. The possible LMT consequences in other systems are discussed.