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

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 s...

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Bibliographic Details
Main Author: Hosho Katsura, Dirk Schuricht
Format: Article
Language:English
Published: SciPost 2025-08-01
Series:SciPost Physics Core
Online Access:https://scipost.org/SciPostPhysCore.8.3.052
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Summary: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.
ISSN:2666-9366