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arXiv · 2506.03668

The Yang-Baxter integrability of the critical Ising chain

Akash Sinha·Tinu Justin·Pramod Padmanabhan·Vladimir Korepin
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Abstract

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.

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Akash Sinha, Tinu Justin, Pramod Padmanabhan, Vladimir Korepin. 2025-06-04. The Yang-Baxter integrability of the critical Ising chain. https://doi.org/10.1088/1742-5468%2Fae0690

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