Abstract
In this paper, we have proved that there exists no translation invariant pure state of M=⊗k∈Z Md(k)(C) that is real, lattice symmetric with a certain twist and SU2(C) invariant for any even integer d ≥ 2. In particular, this result also shows that the Heisenberg iso-spin anti-ferromagnetic model with 12-odd integer spin degrees of freedom does not admit a unique ground state.
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