Ordering of Energy Levels for Extended $\mathrm{SU}(N)$ Hubbard Chain

The Lieb–Mattis theorem on the antiferromagnetic ordering of energy levels is generalized to $\mathrm{SU}(N)$ 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.