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arXiv · 2503.18885

A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain

Hosho Katsura·Dirk Schuricht
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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.

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Hosho Katsura, Dirk Schuricht. 2025-03-24. A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain. https://doi.org/10.21468/scipostphyscore.8.3.052

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