The Yang-Baxter integrability of the critical Ising chain
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917000602714112 |
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| author | Sinha, Akash Justin, Tinu Padmanabhan, Pramod Korepin, Vladimir |
| author_facet | Sinha, Akash Justin, Tinu Padmanabhan, Pramod Korepin, Vladimir |
| contents | We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral parameters. The $R$-matrix is non-local, as it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inverse scattering method can still be suitably adapted. We then recursively obtain the conserved quantities [in the infinite volume] by the boost operator method. Remarkably, among the conserved charges we also find the Kramers-Wannier duality and other non-invertible symmetries for the periodic transverse field Ising model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Yang-Baxter integrability of the critical Ising chain Sinha, Akash Justin, Tinu Padmanabhan, Pramod Korepin, Vladimir High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral parameters. The $R$-matrix is non-local, as it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inverse scattering method can still be suitably adapted. We then recursively obtain the conserved quantities [in the infinite volume] by the boost operator method. Remarkably, among the conserved charges we also find the Kramers-Wannier duality and other non-invertible symmetries for the periodic transverse field Ising model. |
| title | The Yang-Baxter integrability of the critical Ising chain |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2506.03668 |