Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
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 an...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::c62c89fabda5e4225bf2fb53218f0e45 |
| Acceso en línea: | http://hdl.handle.net/10261/428825 https://www.scopus.com/pages/publications/105005980597?origin=resultslist |
| Access Level: | acceso abierto |
| Palabra clave: | Conformal and W Symmetry Discrete Symmetries Global Symmetries Lattice Integrable Models |
| Sumario: | 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. © The Author(s) 2025. |
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