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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Bibliographic Details
Main Authors: Hua-Chen Zhang, Germán Sierra
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP05(2025)157
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Summary: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.
ISSN:1029-8479