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A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain
by Hosho Katsura, Dirk Schuricht
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Hosho Katsura · Dirk Schuricht |
| Submission information | |
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| Preprint Link: | scipost_202507_00019v1 (pdf) |
| Date accepted: | July 17, 2025 |
| Date submitted: | July 7, 2025, 4:28 p.m. |
| Submitted by: | Dirk Schuricht |
| Submitted to: | SciPost Physics Core |
| for consideration in Collection: |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
We thank both referees for their very positive reports and the useful remarks. We have addressed these in our resubmitted version.
List of changes
-last line of introduction: generalisation -> version
-added remarks on injective MPS after (3)
-after (6): Added sentence “Full numerical …” regarding the uniqueness of the ground state
-added footnote 6 on the general construction of gapped parent Hamiltonian
-added a remark on the injective MPS after (8)
-added Reference 40
-corrected the typos mentioned by the referees but kept the notion of a parent Hamiltonian
-clarified the different basis as suggested by referee 2, by revising the last paragraph of App. A and adding a remark after (28)
-added remarks on injective MPS after (3)
-after (6): Added sentence “Full numerical …” regarding the uniqueness of the ground state
-added footnote 6 on the general construction of gapped parent Hamiltonian
-added a remark on the injective MPS after (8)
-added Reference 40
-corrected the typos mentioned by the referees but kept the notion of a parent Hamiltonian
-clarified the different basis as suggested by referee 2, by revising the last paragraph of App. A and adding a remark after (28)
Published as SciPost Phys. Core 8, 052 (2025)