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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| Format: | Article |
| Language: | English |
| Published: |
SciPost
2025-08-01
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| 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. |
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| ISSN: | 2666-9366 |