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SO($n$) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU($n$) spin chains
by Yueshui Zhang, Ying-Hai Wu, Meng Cheng, Hong-Hao Tu
Submission summary
| Authors (as registered SciPost users): | Hong-Hao Tu |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2508.13114v3 (pdf) |
| Date submitted: | Jan. 22, 2026, 12:26 p.m. |
| Submitted by: | Hong-Hao Tu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct a class of conformal boundary states in the $\mathrm{SU}(n)_1$ Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding $\mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1$. These boundary states are beyond the standard Cardy construction and possess $\mathrm{SO}(n)$ symmetry. The $\mathrm{SU}(n)$ Uimin-Lai-Sutherland (ULS) spin chains, which realize the $\mathrm{SU}(n)_1$ WZW model on the lattice, allow us to identify these boundary states as the ground states of the $\mathrm{SO}(n)$ Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the $\mathrm{SU}(n)$ ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.
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Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2026-2-10 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
I used Gemini to help rephrase certain sentences for clarity and grammar in the referee report.
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Minor comment:
On page 7, the authors state: "Remarkably, recent developments in integrability techniques have demonstrated that $|{\rm MPS}\rangle$ is an integrable boundary state of the ULS chain, with integrability ensured by the so-called KT-relation [39–42]." However, as far as I am aware, none of the cited references [39–42] discuss the KT-relation. To my knowledge, this relation was first introduced in Ref. [59]. Indeed, the authors correctly cite Ref. [59] in Appendix B, stating that "The overlap formula for an integrable boundary state can be derived algebraically once the KT-relation is established [47, 59, 60]."
I suggest that the authors clarify this point on page 7 before publication.
Requested changes
Correct the citation regarding the KT-relation on page 7.
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