Properties of the first excited state of nonbipartite Heisenberg spin rings

Systematic properties of the first excited state are presented for various ring sizes and spin quantum numbers which are only partly covered by the th eorem of Lieb, Schultz, and Mattis. For odd ring sizes the first excited en ergy eigenvalue shows unexpected degeneracy and related shift quantum numbe rs. As a byproduct the ground state energy as well as the energy of the fir st excited state of infinite chains are calculated by extrapolating the pro perties or only a few, finite, antiferromagnetically coupled Heisenberg rin gs using the powerful Levin sequence acceleration method.