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...

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Detalles Bibliográficos
Autores: Zhang, H.-C., Sierra, G.
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
Descripción
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.