The Lieb-Mattis theorem on the antiferromagnetic ordering of energy levels is generalized to SU (N ) extended Hubbard model with Heisenberg exchange and pair-hopping terms.It is proved that the minimum energy levels among the states from equivalent representations are nondegenerate and ordered according to the dominance order of corresponding Young diagrams.In particular, the ground states form a unique antisymmetric multiplet.The relation with the similar ordering among the spatial wavefunctions with different symmetry classes of ordinary quantum mechanics is discussed also.
The Lieb-Mattis theorem is generalized to an antiferromagnetic spin-ladder model with four-spin cyclic exchange interaction. We prove that for
J>2K, the antiferromagnetic ordering of energy levels takes place separately in two sectors, which remain symmetric and antisymmetric under the reflection with respect to the longitudinal axis of the ladder. We prove also that at the self-dual point
J=2K, the Lieb-Mattis rule holds in the sectors with fixed number of rung singlets. In both cases, it agrees with the similar rule for Haldane chain with appropriate spin number.