Rigorous results for a hierarchy of generalized Heisenberg models.
The Lieb-Schultz-Mattis theorem is extended to generalized Heisenberg models related to unexceptional Lie algebras. It is shown that there are no energy gaps above the ground states for SO(4), Sp(2), and SU(4) Heisenberg models; but gaps are suspected to occur in SO(5) and SO(6) models. The nondegenerate ground state for these models is rigorously proven.
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Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China.