Ordering of Energy Levels for Extended SU(N) Hubbard Chain

Abstract

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.

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Cited by in corpus (5)

• Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Counterexamples to Ferromagnetic Ordering of Energy Levels
• Lowest energy states of an $O(N)$ fermionic chain