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

SciPost Physics Home Authoring Refereeing Submit a manuscript About SO($n$) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU($n$) spin chains Yueshui Zhang, Ying-Hai Wu, Meng Cheng, Hong-Hao Tu SciPost Phys. 20, 067 (2026) · published 2 March 2026 Part of the In Memoriam: Ian Affleck Collection in the In Memoriam Series. doi: 10.21468/SciPostPhys.20.3.067 pdf BiBTeX RIS Submissions/Reports 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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.3.067TI - SO($n$) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU($n$) spin chainsPY - 2026/03/02UR - https://scipost.org/SciPostPhys.20.3.067JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 3SP - 067A1 - Zhang, YueshuiAU - Wu, Ying-HaiAU - Cheng, MengAU - Tu, Hong-HaoAB - 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.ER - × @Article{10.21468/SciPostPhys.20.3.067, title={{SO($n$) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU($n$) spin chains}}, author={Yueshui Zhang and Ying-Hai Wu and Meng Cheng and Hong-Hao Tu}, journal={SciPost Phys.}, volume={20}, pages={067}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.3.067}, url={https://scipost.org/10.21468/SciPostPhys.20.3.067},} Ontology / Topics See full Ontology or Topics database. Boundary conformal field theory Integrability/integrable models Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Yueshui Zhang, 3 Ying-Hai Wu, 4 Meng Cheng, 1 2 Hong-Hao Tu 1 Ludwig-Maximilians-Universität München / Ludwig Maximilian University of Munich [LMU] 2 Arnold Sommerfeld Center / Arnold Sommerfeld Center for Theoretical Physics [ACS] 3 华中科技大学 / Huazhong University of Science and Technology [HUST] 4 Yale University Funders for the research work leading to this publication China Scholarship Council Deutscher Akademischer Austauschdienst / German Academic Exchange Service [DAAD] National Natural Science Foundation of China [NSFC]