Extension of Lieb-Schupp theorem to Heisenberg models with higher-order interactions

We extend the Lieb-Schupp theorem to Heisenberg models with higher-order interactions on nonfrustrated or frustrated finite lattices. These lattices are constructed by even-numbered rings with or without crossing bonds and have reflection symmetry. The results show that the ground state has total spin zero in wide interaction parameter regions which are not covered by the results of Marshall-Lieb-Mattis-type arguments.