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

TL;DR

This paper generalizes the Lieb-Mattis theorem to the SU(N) extended Hubbard model, establishing an ordered structure of energy levels based on Young diagrams, with implications for ground state symmetry.

Contribution

It introduces a novel extension of the Lieb-Mattis theorem to SU(N) models with complex interactions, proving energy level ordering based on representation theory.

Findings

Minimum energy levels are nondegenerate and ordered by Young diagram dominance.

Ground states form a unique antisymmetric multiplet.

The ordering relates to symmetry classes of wavefunctions.

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.