Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 024, 13 pages      arXiv:1003.2147      https://doi.org/10.3842/SIGMA.2010.024
Contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries

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

Tigran Hakobyan
Yerevan State University, Alex Manoogian 1, Yerevan, Armenia
Yerevan Physics Institute, Alikhanian Br. 2, Yerevan, Armenia

Received November 03, 2009, in final form March 15, 2010; Published online March 20, 2010

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.

Key words: Lieb-Mattis theorem; SU(N) Hubbard model; ground state; dominance order; Schur-Weyl duality.

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