A brief note on the G2 Affleck-Kennedy-Lieb-Tasaki chain
Abstract
We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G2. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G2 analog of the famous AKLT chain.
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