Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
Abstract The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the 3-state Potts chain as examples, that the symmetry operator for the Kramers-Wannier self-duality follows in a...
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2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)157 |
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| author | Hua-Chen Zhang Germán Sierra |
| author_facet | Hua-Chen Zhang Germán Sierra |
| author_sort | Hua-Chen Zhang |
| collection | DOAJ |
| description | Abstract The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the 3-state Potts chain as examples, that the symmetry operator for the Kramers-Wannier self-duality follows in a simple and direct way from a ‘generalised’ translation symmetry of the model wave function in the anyonic fusion basis. This translation operation, in turn, comprises a sequence of F-moves in the underlying fusion category. The symmetry operator thus obtained naturally admits the form of a matrix product operator and obeys non-invertible fusion rules. The findings reveal an intriguing connection between the (non-invertible) translation symmetry on the lattice and topological aspects of the conformal field theory describing the scaling limit. |
| format | Article |
| id | doaj-art-dc5be33baffe4489abdf615ef0ca99f2 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-dc5be33baffe4489abdf615ef0ca99f22025-08-20T02:05:45ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025513110.1007/JHEP05(2025)157Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspectiveHua-Chen Zhang0Germán Sierra1Instituto de Física Teórica UAM/CSICInstituto de Física Teórica UAM/CSICAbstract The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the 3-state Potts chain as examples, that the symmetry operator for the Kramers-Wannier self-duality follows in a simple and direct way from a ‘generalised’ translation symmetry of the model wave function in the anyonic fusion basis. This translation operation, in turn, comprises a sequence of F-moves in the underlying fusion category. The symmetry operator thus obtained naturally admits the form of a matrix product operator and obeys non-invertible fusion rules. The findings reveal an intriguing connection between the (non-invertible) translation symmetry on the lattice and topological aspects of the conformal field theory describing the scaling limit.https://doi.org/10.1007/JHEP05(2025)157Discrete SymmetriesGlobal SymmetriesLattice Integrable ModelsConformal and W Symmetry |
| spellingShingle | Hua-Chen Zhang Germán Sierra Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective Journal of High Energy Physics Discrete Symmetries Global Symmetries Lattice Integrable Models Conformal and W Symmetry |
| title | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective |
| title_full | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective |
| title_fullStr | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective |
| title_full_unstemmed | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective |
| title_short | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective |
| title_sort | kramers wannier self duality and non invertible translation symmetry in quantum chains a wave function perspective |
| topic | Discrete Symmetries Global Symmetries Lattice Integrable Models Conformal and W Symmetry |
| url | https://doi.org/10.1007/JHEP05(2025)157 |
| work_keys_str_mv | AT huachenzhang kramerswannierselfdualityandnoninvertibletranslationsymmetryinquantumchainsawavefunctionperspective AT germansierra kramerswannierselfdualityandnoninvertibletranslationsymmetryinquantumchainsawavefunctionperspective |