Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908374528950272 |
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| author | Zhang, Hua-Chen Sierra, Germán |
| author_facet | Zhang, Hua-Chen Sierra, Germán |
| contents | 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 | Preprint |
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arxiv_https___arxiv_org_abs_2410_06727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective Zhang, Hua-Chen Sierra, Germán Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics 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. |
| title | Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective |
| topic | Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2410.06727 |