A brief note on the G${}_2$ 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 G${}_2$. 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 G${}_2$ analog of the famous AKLT chain.

arXiv commentIn memory of Ian Affleck

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